HighlySmooth Zeroth Order Online Optimization
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Formal Metadata
Title 
HighlySmooth Zeroth Order Online Optimization

Title of Series  
Part Number 
5

Number of Parts 
10

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2016

Language 
English

Content Metadata
Subject Area  
Abstract 
We consider online convex optimization with noisy zeroth order information, that is noisy function evaluations at any desired point. We focus on problems with high degrees of smoothness, such as online logistic regression. We show that as opposed to gradientbased algorithms, highorder smoothness may be used to improve estimation rates, with a precise dependence on the degree of smoothness and the dimension. In particular, we show that for infinitely differentiable functions, we recover the same dependence on sample size as gradientbased algorithms, with an extra dimensiondependent factor. This is done for convex and stronglyconvex functions in constrained or global optimization (with either one point or two points noisy evaluations of the functions). Joint work with F. Bach.

00:00
Point (geometry)
Group action
Building
State of matter
Constraint (mathematics)
Multiplication sign
Direction (geometry)
Similarity (geometry)
Insertion loss
Function (mathematics)
Student's ttest
Distance
Sequence
Expected value
Maxima and minima
Mathematics
Goodness of fit
Manysorted logic
Convex set
Subtraction
Units of measurement
Condition number
Order theory
Order theory
Addition
Statistical hypothesis testing
Scaling (geometry)
Gradient
Moment (mathematics)
Price index
Mathematical model
Mortality rate
Sequence
Functional (mathematics)
Field extension
Arithmetic mean
Stochastic
Lattice (order)
Convex set
Function (mathematics)
Right angle
Mathematical optimization
Matching (graph theory)
Resultant
Directed graph
08:49
Group action
Greatest element
Linear regression
State of matter
Equaliser (mathematics)
Decision theory
Multiplication sign
Range (statistics)
1 (number)
Expandierender Graph
Parameter (computer programming)
Mereology
Weight
Grothendieck topology
Glatte Funktion
Expected value
Maxima and minima
Plane (geometry)
Convex set
Square number
Process (computing)
Spacetime
Product (category theory)
Rate of convergence
Gradient
Moment (mathematics)
Logistic distribution
Thermal expansion
Mereology
Functional (mathematics)
Maxima and minima
Flow separation
Category of being
Hausdorff dimension
Right angle
Figurate number
Resultant
Point (geometry)
Computer programming
Statistics
Free group
Link (knot theory)
Observational study
Civil engineering
3 (number)
Wave packet
Frequency
Inclusion map
Population density
Average
Wellformed formula
Lipschitz continuity
Energy level
Glattheit <Mathematik>
Subtraction
Associative property
Hydraulic jump
Linear map
Condition number
Order theory
Compact space
Numerical digit
Lemma (mathematics)
Volume (thermodynamics)
Line (geometry)
Incidence algebra
Mortality rate
Estimator
Field extension
Voting
Glatte Funktion
Network topology
Noise
Gravitation
Game theory
Object (grammar)
26:26
Beat (acoustics)
Musical ensemble
Curvature
Latin square
Multiplication sign
Connectivity (graph theory)
1 (number)
Mereology
Event horizon
Rule of inference
Power (physics)
Number
Expected value
Square number
Subtraction
Condition number
Addition
Order theory
Theory of relativity
Gradient
Independence (probability theory)
Division (mathematics)
Mortality rate
Estimator
Vector potential
Lattice (order)
Network topology
Hausdorff dimension
Object (grammar)
Flux
Gradient descent
35:14
Field extension
Goodness of fit
Closed set
Operator (mathematics)
Multiplication sign
Right angle
Thermal expansion
Bilinear form
Directed graph
Number
Power (physics)
Estimator
36:51
Frequency
Goodness of fit
Summation
Lattice (order)
Prisoner's dilemma
Multiplication sign
Gradient
Expression
Ring (mathematics)
Units of measurement
Physical system
39:02
Point (geometry)
Axiom of choice
Slide rule
Musical ensemble
Disjunctive normal form
State of matter
Multiplication sign
Parameter (computer programming)
Power (physics)
Frequency
Square number
Energy level
Position operator
Condition number
Physical system
Addition
Chemical equation
Expression
Basis (linear algebra)
Infinity
Bilinear form
Field extension
Angle
Noise
Object (grammar)
Arithmetic progression
Resultant
Directed graph
46:55
Point (geometry)
Slide rule
Standard error
Free group
Decision theory
Multiplication sign
Range (statistics)
Moisture
Routing
Chaos (cosmogony)
Parameter (computer programming)
Inequality (mathematics)
Expected value
Glatte Funktion
Frequency
Goodness of fit
Centralizer and normalizer
Casting (performing arts)
Average
Square number
Subtraction
Position operator
Condition number
Physical system
Addition
Order theory
Focus (optics)
Spacetime
Concentric
Prisoner's dilemma
Gradient
Physical law
Division (mathematics)
Set (mathematics)
Line (geometry)
Functional (mathematics)
Proof theory
Summation
Voting
Lattice (order)
Phase transition
Noise
Right angle
Game theory
Object (grammar)
Resultant
Local ring
Directed graph
58:05
Point (geometry)
Musical ensemble
Multiplication sign
Direction (geometry)
Decision theory
Similarity (geometry)
Routing
Parameter (computer programming)
Inclusion map
Goodness of fit
Manysorted logic
Energy level
Field (mathematics)
Associative property
Position operator
Units of measurement
Condition number
Process (computing)
Gradient
Expression
Set (mathematics)
Functional (mathematics)
Local Group
Field extension
Summation
Arithmetic mean
Combinatory logic
Hausdorff dimension
Universe (mathematics)
Noise
Right angle
Game theory
Local ring
00:06
and we and Hong Kong in the world and the world and because of a slowdown "quotation mark the owners of this indications lists so the people to be here "quotation mark increasing Pacific race and I have to say that this is a don't reserve Francis might and then there was a and she wanted to talk to me be on the source of the of twisted conditions and the banal and on May 9 as Israelis is that we're going to focus on functions so we want to do condition of comics extinctions that are very very small so usually what they mean by that and I was at that OK so we what's with some litigation so long as the data suggest you have lots of 51 stated 1 of them has a different meaning and I would want to do is just a good quality condition but the main idea so we have a mapping S which is comic books and we want to optimize its earned we we'd like to assume some of the United dysfunction that is a pity that the 2 sides arrest Muslims Wilson and finally the anybody is that for always the victory of 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welcome addition was that sort of thing for a while I am motioning the holds this or most commonly later on tradition because I treated better results would affect thing warned me that full funding of which 1 it's but of another 1 was awarded data online for its what's on my intuition tormented mission is exactly the same thing as just a goes to get the convexity execution it said that the mapping effort that you want to optimize the statistical expecting that you can't change for banks dismantled already museum and 1 death but when you make the is with the F 1 the news media reinforcements and on and again so we have saying have a sequence of mapping will have just 1 thing after the other circuits of being F1 F2 with 3 and when you make a great X 1 you get us but if 1 of affects 1 or if you will it's not enough condition but only the NYT the gradient of F 1 it's 1 of the vision of F 1 6 1 but he savings we're going to assume that we just go we can only contribute to the value of we 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difference between pretty rough minus the best lost insight into an issue new amendments the original function f you will have a to extort state for the end of the scale but this is not exactly a bandits follow that knows what his Budget Committee conditions this is not because in it's weird to begin that exactly is able execute here I'm just assume that except she has to be constrained said like inquiry might come from anywhere where I won't get into that has to be in the articles from Slate X clearly
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erred for this that the site was just too good to define what is that a on 19 nation but to be resized from the will not speak a lot on my tuition at home give us just a little mention that I can do it and trees so we see the results of the that we have in to the kind of comics Olds for online on my intuition that for free In an interview with you I mean know we just short of 1 side of pools you why everything that I said or rejoices in college tuition also on 19 traditions and the trees to be even more precise was the wife on magician is actually simpler than questions the incident but so that the data we have also had the strong title he had this month spoke about political extradition on 9 of sedition statistical conditions and with you data that made precisely assumption the 4th 1 is so In that ideas of most Hammersmith and we also we can make the distinction on them on the Commission the overlapping so this is not an artistic and political explanation we can assume so we have 2 types of assumptions that the answer to who before the comics politicization poor the 1st type of assumption is that there is news from the complex as the 1 is every tool was this is is the same as social except that 1 signed here is beyond the it's not that the US and beyond the oral or equal to Austin like this let's kind of your permission for the 4th 1 in which regard being mutually comics I want to be Gates said in 1 dimension you you commit that demise would be a 1st only collects news only collect if the solidarity of is other new so you know that the common opinions by visions also reflects but here because when you Newfoundland excellently on more than Sligo Next IT S U 2 for the tradition because you that wedding F Israel and monitored by quality down the wrong type of persons and that what we to match will not on the it is the smoothness and the beginning of the year that your annuity which is commanded us to look at what was lest it means that you're gradient is digits forested otherwise that you can but the wonder mapping asked by you and I know that when the product of so it short of Newsweek expand move your mapping effort is reliable and advise whether down an opponent byproduct and both of these functions as you and they can get to the factories of and the question is can we use this kind of assumption in statistics on Michael execution with that was all the feedback to work in Britain where yes used in this way a full line of here because on the next flight and of the new tool that we have something different like a free and I would put a freaking out to skate said Wednesday would it's as France's very careful often have allegedly dignity of your of em game because if you look at it and we will use because wireless New Square is the the yes because he had not because he again on August producer lending there is presented that and the need to look at the at the end there are various home the functional only collect some and began lowlevel 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initial assumption that under no hot wet wet weather with only and without the objectives so the following it with the describing what our objectives that do a bit of you the judge on the difficulties and book so the first 1 if we if we are to blame ,comma situation without knowledge and with access to the region so it's not a whole lot of looking here but just gets on some intuition so if we're looking at a real access to the region's to looking at the fundamentals and that there is no noise we can find and when the team out and put in Portland itself cannot may further to minimize the question which is a significant so follow that don't know it sorry about that said that at some stage mother from mutilating F is a is in the Senate Sweden wrecked the new greatest some Dodger Serena got the right answer and then you know that the murals have reasonably to be licensed as it collects on the bottom on the left parts of the year this century the canvas tent this part of the history and you will know that you during the train a ripe opportunity here and assuming that there is this case they'll give into the flogging this so we win shape and willing to work to expand it as a find of Switzerland with icing that contains it and I know that's as an experiment in mainly was due to be in the range an aide to persuade rechristened of hazardous initially checked out of a avoidance intervals and if you look at this and was all of this account of the need for you into a little to be laziness Volume decreases mickelson sector and so your your your comment that the Nunavut but this has to be over that more the John noise it's not working so you have to graze within is important and it will never what we as almost in a lot of new cinema or you won't work with a magician so we will not look at that kind of also of picnics instead we want look at ways means because the company itself was pretty well with online on education when I admit I don't know if anybody knows but that was is that 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resplendent in 102 square but you once most of the fighting adding the assumption that appeal mostly to other social adjustment the correct then you get a residence in 1 of the 21 community and if you either both of whom some Jewish of most ministers publicity that the rights of the density of the 90's and that is that you that's when you have a moment when you add smoothness and simplicity to the program began .period festivals and without this assumption authorities are alright is blue sensing a statistic assumption the statistical tradition we as was also the feedback so vilified again vegetable products went on to dust access will point to the to the benefit of effort at a point the mother of his usual level as it is clearly oral arguments which is ambiguous that says that if you in 1 dimension and you're trying to estimate the weight of F you just have to Gray F of expresident dominance as a figure of minus F of X minus dollar up and this is in that there is a good deal of this very small this is exactly the right out of this sisterly fools but so did say that you could greatly could get to play against 4 of Ethel freed does by using 2 degrees all of degrees depending on no I wasn't so the rest of them from center said that she is .period made today that made so this is great when you will have much because that's where the noise everything about me this is this is the moment when you it because when is that thing about light site on him and media made that balances his look at that so this idea is sure of is when you almost certainly will want to use it as With the bank was there is it is also limited days away to choose from this kind of pull them out and using the Associated trying to mediate the powerful salami .period using also of the this is a way to solve situation using the who was also limited and in 1 dimension is quite simple actually so let's say you love you gracelessly points here and there is an estimate lights and it shows you that will most interesting that's the value of abortion it is like this so I knew no 1 is worth 1 you know that the new information is going to be in that that part of the brain In this weekend we will try talking to the spot here is still as a free .period the secretive feeling that it was gray increasing you know that the new actually to be on that last part of paying him so To begin here when you doing free trade the time you are you are going to lose take the remaining states space in 2 so this will give the Norris of Clinton's and is calling onedimensional utility beds if you can let because going to buy a researcher with emergence of it's easy the 3 you can do that in the in the light of the mansion and would get the narrative regions but the issue is absolute collective residents or the Boston Tea is chiefly by 7 which is preachy still when you when DVD so we are not going to use that kind of missiles but we could between unwittingly till the year the the fickle state of the science is actually what their role here is that when you're going from 1st of doctors also at you just modify your rights of creditors by the beginning with gay because instead of having the needing 1 created it awakens would need the query to get rid of the state of the wind so from 1st to the also document evaluates it's like if you we handle into the picture and if you look at it upholds its and putting it wasn't studies so we dined and certainly after Greece about Anderson .period wages alliance where is the favorite thing simply walking action since then willing to look at just about ingredients said that instead of observing radiant the Gulf after you have so many nationals is greater on the ingredients is exactly the same as possible in this and said that you know bulldozers invented the printing the multinational Britain there is a wallet on this please well the fear that if you the mightiest the estimate of 2 reasons that means that if the expectation of the 0 and is very possibly the least Mosquera to those gravity and then you can get the rights of regiments of the adults gold of unity if we have enough political extinction and if you have if we had as many of the comments assumptions and the rights of legends decrees increased control of to the deal that and assuring them that the plan which was quite a long time ago if you remember the results of vengeance we don't know is whether Samaranch encourages except that instead of having to you we had a 1 gets was built of quality and 1 22 became will from lawyers to Wednesday solicitations without again interview I favorites occurred by so when you will farms also
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dealt to 1st order you will fall from fossil which is also the only Peres maybe when you move from Lazio to Beresford and made so the question is what happens when you move from 1st of all there are no a was also the only 1 race and we expect that McBride's arrest of by deep under the by square and this is exactly what we are aiming at aiming at so this this lies in the summary well what we what we know let the 1st frequents gear we know that the directive and that we are not aware of that's what we aim at McCain so if we have a floating at the division of political extradition there will sell and noisy of local extinction we're looking at is the failings "quotation mark of the this idea you would be conducive to that baby having lost interim maybe we're looking at slow times this will achieve a sensing here so that's what we would like to to work there and that's what we did which is the same Sembiring but still it's pretty 1 because you can't see when with isolated India they could be that we in the scramble moderately Monday at this is that as the Douglaston GTE should be there is 1 of the garden because of the depth to is 1 so what we get is that we get with graduates match with much much the same objectives it's that it all that much when based more fully discussed that meeting is to move but not with most of the match for sure but that is when mapping I think that it is most we recall the rest of the evidence that we are aiming at the polls and you to finish the year that because there we had told you what do we know where this is going to be solved on ones you was suddenly is noisier conditions so we know we don't know that this is called Dusty is optimistic beat Friedel gets in there and we know that we can find and was so that we get the current events and pretty deep in the scope of the magician that we don't know the department's and here we we we we Haiti I'm at having presence in the context of the 103 d with him at the England so register essentially flat that meeting as Tony and smaller then we gets this quality that's but the going out and selfimportance was wounded if we have only wanted to assertions .period economics also was less than we get rid of that has to do to me of 1 film is shown equal wasted 2 minutes 1 and actually or deposit USA that shot only the Commission to get to the way of a spilled of the button to bribe I look rolled to and this year's began commercial service that ruling at the when you look at that the president on down is not scope of the it's around utility get is a small but growing tried to today's debate and I think Wendy is 10 book would not Dougherty is funny but it's exciting to be to be a lot more careful to India so the look noted that he is deals scope of let alone would have to White because I mean that the petition material and if the EU have always sought to to it this fall or you Monte McKeon listed actually community here then it's not true but if you take the which is I think you but at have done it I think it's been expected to be Bentley 1 rather than it's still looking at the minute the for parties that Uganda imagine the of I also attended a number of the signals that the expenses the blown arrived animal in the future and its have that I don't care for because it's in the audience gets people have to be at the movies it anyway so not all of 18 years 1 of the the side of the canyon imagine this is a 190 that's a minute before the but stated it is a major component and so when we under the protest was so this is because political Finley in the name of that gets the more it writes Tibetans but somebody can result in an instant so again we are aiming at having is exactly something that the president was the square look but is that all objectives to get that supplied don't we won't be able to get it get them but we we can't principles .period I will as have you maker of Nora today minutes in 5 minutes that nite please but so you're wanting to do to Latin wheeling 2 days told treat that going to combine and the 4 for New Year's morning on the morning that that things just the way through the Mediterranean Sea and the other 1 is a way to move Europe was even more limiting the power already clearly what we would like to work to use greater missiles for a foghorn and that issue is that we don't have access to the wind would just have access to the meeting venue of F of X so we have ever of the living specimens but we we have this time in this sector of various the majority of mission gradients into the book would before we know that in 1 dimension F of extra that I innocent ever of exited the little is known as the result of of of ever exploits in the day's more useful and when dies the smaller issues of most but the thing which is quite surprising victory this difference here is exactly the radiance of a function f that Bell which is almost as tho that thing is almost to the recount of death but this is a remnant of the mapping which is almost as this is a way out of climate that dealt with the adversities as part of the dollar as prime is that function you can and if you look at it is that if petition over zeal of death of expresident that he would not win Rosabel you need both it if we're minimizing and tho we we we would have we can't get out of the bias as middle of relative of and that Dell simply by boring and sirens Whittier presumed performance 141 ads and putting Jeezy to be F of experts inside and that does bands of sand on the bed the debate about because of that the indemnification of of that thing is exactly the same for this edition of GE is exactly the right out of the strike was embarrassed the 5th part of that I was embarrassed and if you look at the science of throws Mitoji it's on the order off 1 of the best way so if you have to do is to get the gradient descent with respect to edit since then the independence is ugly to be wonderful 250 times the 1st love edition of furious made also is 1 of the top 3 is 1 of the best possible 250 but he I looked in my eyes and that binds the default amazing F the NHS's out particularly now that battle the tree your to be order their doctors monitored the scope of the and it should demand that I would get 1 of 2 2 1 4 and this is exactly the idea that mission of flats and is closer to but this is this is the idea of a mosque exactly but I think old earlier I that this is so this is this idea here is the 3 due to a newest unity as the so if go from admission went was deity we have the same the same is an idea that say that if you look at the potential of that guy here also on the union's stance will not be with mission we have something at Centinela performance once so it's something utterly in its industry on which someone so if we sampled you the unity of the mission the leading the Sendai the investigation of that thing is exactly the gradient of and that does so this is always the rate estimate which is exactly the way down to the meeting which is almost as and so this is a variant of and that power and that dot Is that expectation of born of of almost and we introduce implications that so there the violence of that is the notorious wanted by discovered at the square and so we should do exactly the same criticism accommodations
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at him this disease that is 1 who did the right of graduates of the discredited them to borrow 1 4 flat as sources say this is a reserved major due to me most unions and infects mind and then news again by us on new battle automotive people so we note claiming that we that's that's false ID number for the future the idea is to work to combine it with another retreat and and is
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seeking to use the tenant advise on so I don't want to do that because remember that on mapping where there let me that mapping effort yeah we're loading Evansville was very closely to the expansion to F of Xpress a small power is there is close to its original extension so it's a very close to bring in in the in all and it's true that to alter does a leading to introduce chairman of Kane said that's when you integrate case against are you get 1 a new indirect jails against all of those operations get 0 and can you gonna have explicit form for this for this kind of John and care for this year can go to them the other is twofold and will actually land because if scanners and the euro integrates F against at all times came you see that that guy here it is critical that 2 what can I is clearly is so we have a pretty good estimate of Africa which is about to admit that because of the delivery eagerness to make as before when went into
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using this this type of techniques we have an interest maker of of about 2 . that up here we have
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an estimated that although deducted because of it so we can use it it is about that that is the most of To too good to dismiss lawyers makes again by Bundesbank by and get a very very small percentage emission of effort of the lot that that lived up to that died in today's prison this is actually pretty small so this is this is this year I did his Janet endit we do so if we
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combine both the most restrictive so if we want to use a manifestation of the gradient of the of instead of from function Durenberger said the trick of he said OK we have a good weekend of bitterness teammates of the Minnesotan function which is close to an and here we would anything except as a function of disposable effort is going to be different .period less than the sum of the system and the system it is facing a new use incentives for use on piracy on the new and you couldn't ever of experts all about the and then to diet might have tired of the UN demands is against your own can and if you look to add to that that guy here yeah that's a function and it should just come the ring of the pension to rent out of every other top is exactly given by laser visit from so this gives you and bias in the middle of the S L the and this and this is not so that be up pretty interesting because I said before the effort all ended up is not only cruel to ask that that will with that that should be done so here we have a meeting which is mediating truce to end and the units are also very very close the debate of Of of it all the time is very very close to the end of it but he added that governor's 1 and that's what you can and to and if you threw a few computer can have diseases those expression
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you can come should also stand here all day and nite and 120 is only something where Abdullah meaning to the phrase With this so here are the only thing which is the we choose a better it's difficult to make it gives this decade is out of my being here that we've defined him using genetic is not necessary context this is a kind of America but it's still amused comments of his newlook tools from economics is his Newfoundland calls for understood collects isn't Advisory Board With the weekend due to a room we can still you use it's pretty festival to interim progress of editors yet we will we will industrialist and a bit of statements but we get a chance to but so you uses the state's strong only if there is a new storm ,comma flights from Europe to tools only collects is at his new Nicholas survivors of yet so if is not only collects them as pointed out is newer to context so it is new is comics but if that is that is not from the comments then ever thought about is that this but that is not a major issue for this will be to his political system it's going bit value and that 2 1 in the residence hall the University sodium yes this is so that's not the main sitting point of view this is just a remark and get it with ice tool vendors in its context but as we are looking out for me that would be honored freefall 5 Infiniti then is the but still we assume just remark and additional day at 4 4 0 4 0 4 with so I thought it through and it lets users both rigs and Eileen then we don't want to do it those divestiture written dissent with respect to that in the middle of of already and so we have we have a tool Maine and was and 1 4 0 in the book value of science at X compact then we can agree at at this stage when make when greatest stage and we doing this written so that's exited XT is 60 minutes 1 breast miners with incentives that size balances estimated the regions we just me is smaller a actuation of death and that is what I was going to use it as a win at his uncle's friends when into war with awards at me all the history is on the mend after each quarter steadily to make degrees F of X 1 DNF of expertise With an abrupt diseases which because if it's nice are looking at Madison noise at state in which we can send out but he was at this time make a great in the binoculars so the noise is still here just to be here next on that point if you're going up if we we wouldn't you if you want to do work on annotation it means that we can operate twice for the same function as do you that I was so it can be discussed was it's a liberal not if it shows that it's not delivered news uses his was became the 1st 1 through about going great twice as important as any queries only once in the function of the season China he is whether or not the issue is at a new industry once the new routine at angles and conditions for it on the other United Online nowadays and you you other than sensitive the country's instantly as because he was almost always wrong and askew you when you make a lot of mechanical 2 points and you can kiss instead and then and nowhere is limited it's not about to modernize its modes you're interested but that's that the main and wasn't and then the choice of all bombing to be again of the that the offkey also saw the toast of parameter in the traveling through burned on the year on the basis of seminaked devotion is registration official mused economics on what without be looking at this and additional not the choice of climate or we change we we change so and to detail all resources trusted by October for instance is looking at Newsweek or makes an engulfing nation we have explicit threats of releases distrust of permit us to the solution used the step in the custody of any of the conditions 1 of the team that suggest a choice of 3 forms when you function and the size of the Of the year exploration acquisition of expression to date that the husband going be driven on the shoulder you can find this is not that big and the idea that there's a reason we just have to deal was you rich .period Bricker reading and this this algorithm gives the always scale as as we wanted in the deaths of on he to by 1 of the wearable as a ghost 1 and that was we don't get it the international films that scale as the desk will on and be basically music presented to the 1 that was sold when the diversity of the the the I think you need foreign authorities have you it's like a consistent because you we have a power and a bit of broker to whether because it said that the so we have a bit of the so they started that has to be a new but that the U.S. has to be or not to to maybe it's that I think is a result of the cornerstones of the case against them but being being being really becoming any bigger is OK because it means that you all that most of economic and reform of voice of of bringing an XT you can you can get no prettier precise position of 2 regions migraine points that are farther away from Europe from Georgia .period Gay Benetton which is the same for instance that demanding is our villages it's not good it's not even if it's in our can get a pretty good of which made a few written by great points that are farther away from X right but this is of ocean which is beginning its most it's almost inevitable in the ladies gives them great follower from your from your point a precise position afterward instance sinks were on the way to interfere is if you looking at square of plastic foam level the precise objection of the regions of verdict from going great .period Jarreau Institute at percentage in May news is usual listening to the radio what that says None answered it such
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years of this slides is the a confluence with unified elections must decided within a single life but this is just too hard to make a point at the end of the Cold so
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this is about the size the war proof of the prison use of the president that wasn't so this is that it's only 6 main arguments and under such a pretty when you move away from me I was going position is pretty natural so when you when you look at at its individual GAO the size of the 5th the point so just looking at the whole Eckstein moves away from X and use your and wasn't too sure that this is the way he does explain it and this is this is some of the fall here you have you haven't off down the tube longer by using expectation and you know that Europe that could use more here you and you have this quantity in Singapore and is my expected Shimon is a gradient of effort that there are so you can pretend you're variant of and that all Hollioake considers this a new gets a diseases simplicity you get that type of thing equity get so I'm not going to talk to down when you have the stuff to down here if you that and you can around the stem and divide by the MIT and it's like you get at the end of this year all made but OK so that the understand when you see that everything is wary of extreme interstate system is when the spaces of even when his x you doing all your Achilles free and it's like a stone or wondered why should it's not that difficult and against those of vessels and his the idea just should get to be 1 this downhill in Orange is a to that 1 here in Orange and all of stamp is going to cancel out when we some of the dominant to out and will be left with is the sum of all of those guys came and this is exactly what we went through which we do hear song the other son of dominant them and entity it is a note that says that if he should be allowed follow at all additional cases and I mean I don't expect anyone to follow that is the last of the 5 something that made the digital cinema that cheating you will and that we are we arrived here on and that's what .period we are here and we're now and a stage 5 of the pool of local excellent condition to begin with we would we say that OK so he I am so that could be more honest consistent with who we are what they have in years and a range of values Sholapur extinction and I know that this is the beginning of the end of the year verification of of the average focus on the quality of air for him to show that that guy is bigger than ever as the average moist came and this is the last day at the office of the storm not proof of committed conditions but here if we don't to Malta's the polluters this is that final address remove that chemical don't go away and just look at that guy here what you see is this is exactly the regrets what mourners the regret their decision at the end of that that he is the leading edge of the debt is acting head of the yeah that was due beginning average of the committee Russell president of regional vessel when it when you're doing to college conditions they say that you using other said last that the pool if you use the battle fortunes comments before that Europe regret treaty is bigger than your motivation at all and so if you want to really get results for the regrets of major mission just needed to be simple but instead of fewer than going to the last thing you just stick to the stage fright so on my intuition is you can get the central father situation except that you're going a onestep less this localization of them when I vision is simple :colon commits position because just did onestep blessing of course and that's that's the the key points of the slide is not out of danger .period because the weakening of the Letterman at which is a fight but this is to show you what exactly that during which arrives here in in the pool under this government which completed a community regret and to minimize your and there are also included proof is quite he's quite a that's that the treaty if you was so if we're looking at some of the Flanders political Max and concentration that we're looking at the federation they would like to use the 2 points altered .period metabolism gets elected stage you you integrate X there is 1 president of the volatility miners dead Argentina the difference I knew I was from issue you should be to send us a deployment of mourners and Luisa from originally had the same kind of residents because they get the same results in the constrained and unconstrained nation it said that foreign cultivation we need to be able to grateful .period put twice its functions at this stage so that we can you can choose and then OK so here just so that a lifetime of if if we are really is my meeting US 101 if we can also the improves is recipe because then it would be this festive lanterns additional video absence of sniffing sensing if we have unequal collection costs control of the city pirate we do get the results on a train and and if a complex unconstrained another set of parameters don't believe me or the people with the union thing quicker and we we don't we don't get together with the president so he was I'm glad the objective of the talks so Minnesota fell frequency are is already in on wheel that if we want to ,comma condition and we still stored on laser lesson we have 1 of the good of the if we hadn't always went by made the floods also don't make me so we yes I think we not only want to give that that if we had the also built the noise we should have the merit of adopting these qualities this community marital problems maybe in some way natural the Poland game and let me get is that we do get a lot of good but up to some of the people out there which is good because for once when the guy with the utility which is the case we are interested in if we look at news from Avonex sevenstory wanted annuity had devalued the unanimity and then we'll be seeing that interact with voters in this government the and we don't get them up to Singapore which 1 he also worked well in the future and is useful for a committed additional another thing before and the flying this is also tool for a 1 9 1 9 9 of 2 nations is Joseph justified it does we would was that 6 we just stick with almost includes defied market including get the same
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results for 1 9 tradition and and convicted think on time by was there was furiously at the University of objectives and would undermine wizards of industry thank you few of in the Iselin the sum injectionmolded yet it is this assuming smoothness the source this information so there is no solution is a new conjectural so it's a quizzical conditions again assuming that I so it has to be amused only collects I don't know this actually is lower bound for the 2 In you strongly contradicts the functions of the National this year on aid even 0 ordered same sending that you considers the cast order the the conversation strong ,comma his functions here is a way out but I think I the final it's the answer 1 of their rights that's that's easier to read so I a at the at some of the the Indian still chaos to be a smooth but I'm pretty sure that this of regiments is not conducted in Italy because here we we we are we going all year because we don't agree outside the debris outside the home the conference at the holes in the names of the not that I don't remember that actually in those those positions on analysts in 1 case and so I don't remember why the on December the on the of dissenting in and view of the individuals who have the right to use it as a lot of this tour we ought to hold on to his wrong route yeah I did slightly concerned that the law will construction uses function which is actually more than that because I think it's 1 of the keys were confirmed but that we have we can we read we have is that no error because I do remember that this discussion in Singapore and the 2 EUR euro giving lot as this same but I don't know why it's not the same thing the days there's so we we we we could take fine but this is sitting at something and I think this is the idea of that is because he gave look at 2 of the good that if you look at the competitive nations and the EU candidates with a vengeance give opponents situation the with when at will the idea that we reject that I was at from 4 bandits this is that way phase is not bend and I know that was the way because this is is a square the guy and that's before editing advantages in this would be incorrect doing bonded didn't condition but it to you you will need this of authority work and I think our sitting in between and I don't understand of the in 1st line the owners readings In the solitude right the race the race last 1 that's that's give me that I was too yeah that was then this is the day is bigger than the 1 you don't have context so far he has refused to the adequately in the news simple actually with the little pools story here as as
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ordered by his to will be of no news from the but here and sincere I'm just using the opposition of Best Buy and that doctors should be as all the value at the end but if you use it at the beginning of the new Kansas pools with With the essence of their father done at his comments if you don't use efficient exhibition at the beginning and then you get an exotic sigh off down that the proposal with along the way on but you can still do it did we not willing render something collecting from knowing BritishAmerican extension was 2 this is my friend and the where the magic comes from the Secretary promised that essentially you know it was going to be solved the know it's but the die is actually a sort and competition latitude location greatly and that was Virginia we get wanted I think competition and that this idea be Douglas to Alacant good can go to the orbiting many industry Sorrell the rest of Canada ancestry but that's the that's OK then that that that you can added that pneumonia but thing is if you mapping out a rigidities most of you know get of the euro and you have this by Azerbaijan's freedom and it is useful to know about it is most even with the double did you can get a very small violence in the world give them dynasty made off of the year of the sum the gradient was more of a wizard for bias that those were biased and until other the violence then again or others at all was on the lawn of course but you your Europe for the FBI's France's is is improving and wondered when the time is important this year but others it's because of the it's it's very about EUR euros the function in New York to make its case most then we can get new alliances or otherwise borrowers will borrow the banks with it's always something the military has apparently there but it's very good that's was a cushion of the handsomest I'm so I I I guess the good news the violence intermittent to to impose that was between parties and and that amazing according to the directive is supposed to be played by the end of the Hornets please no yeah Minnesota but that's a good question will you could make a lot of on this occasion we go solo for some of the new deal with this kind of of session weekly could result we could impose the rights of those words of France's you assume that the so since some kind of ideas the assume that they are complete normal something that and equally equally pools of was approved and I think I think you have to rewrite to make another set of assumptions like like mentioned means will face or no that the based contending for of the rest of the dozens of those techniques indeed From the duration of the inclusive local associations in Washington in what form the whole because the of all markets similar functional was controversial and people on the at the combination of these 2 functions .period ordering both human the utility also has 1 of the 1st Boston's about this this and this and this a very emotional literally around the world and you who currently is still the exchange was all the fault of the simplification it is only after all is going to have to what is your intuition if you're trying to the cooperation is 1 of universe functions of the something Gruden is small compared to the rest of the whole world is for the importance on the route we should so it was "quotation mark decision to use the the dimensions of growth almost all the groups all along with the military coming of alone the people of this city is that all want managers of receiving mediation underscores because the growing the government is using all of but I think at the White Witch's Well if I if I you very functional demise of to not can I can the position of it which is infinitely which is noticeable Simon and cannot find enough and the Commission of it which is in the field was and then uses that can affect weather on entreaties most function to move on In To demise my my my with officials of which mean that you have a function at the beginning that Lotus Award for example patients for launches you or what it's then than its follows mystical function and all the fulfillment of this crap because given that initially job that's as a means of but a with each which units more than trying to work opportunity with the very most so function at an emotional this that some the best I could do that kind of person who uses his vision for America and the evidence might want my and my concern is that if you show them the debate on the battalions but you have to move forward all your own you and the timing on your directive are increasing and became the only city but is just too on the best of your people and the because increase of more than EUR will lead to more office emissions than you would get from the defendant's guilt has shown itself the expression of the will of the people of all European so this is only be dicey and effective not that that the back game because so little is here we just use it here we put into and beat up but if you don't know it just ended just take it for 1 for instance and instead of having it inside this nice expression and tonight's borrow it would just go outside was a regular 1 or the other the poor which is 2 of them and nice so if you don't know and because it's OK the don't both use it it should only be done then it's more tricky the traditional or be that which is a smaller level and the doesn't use it will be at the weekend somewhere that was a I want residual because most then your listen because most wanted for instance of the real resistant to most central to most ended up to be done but you just know for sure that 2 of these at the time of the level that you can use it all I wanted to get because of the argument I said before his show 20 thousand EUR within if you have no idea how can we find that vandalism I don't feel became an instant Schoonmaker created at 1 point on the shore of whether you can maybe get condition it's the toughest in not the usual no don't want to make India a chemical known of known this was noise can teammates Let's get this economy is mandatory for all of us it is the fewer B