arXiv subjects

Vianney Perchet

Publications and source records attributed to Vianney Perchet.

At least 73 records · Page 4Linked to original sources

arXiv2021

Privacy Amplification via Shuffling for Linear Contextual Bandits

Contextual bandit algorithms are widely used in domains where it is desirable to provide a personalized service by leveraging contextual information, that may contain sensitive information that needs to be protected. Inspired by this scenario, we study the contextual linear bandit problem with differential privacy (DP) constraints. While the literature has focused on either centralized (joint DP) or local (local DP) privacy, we consider the shuffle model of privacy and we show that is possible to achieve a privacy/utility trade-off between JDP and LDP. By leveraging shuffling from privacy and batching from bandits, we present an algorithm with regret bound $\widetilde{\mathcal{O}}(T^{2/3}/\varepsilon^{1/3})$, while guaranteeing both central (joint) and local privacy. Our result shows that it is possible to obtain a trade-off between JDP and LDP by leveraging the shuffle model while preserving local privacy.

cs.LG↗

arXiv2021

Making the most of your day: online learning for optimal allocation of time

We study online learning for optimal allocation when the resource to be allocated is time. %Examples of possible applications include job scheduling for a computing server, a driver filling a day with rides, a landlord renting an estate, etc. An agent receives task proposals sequentially according to a Poisson process and can either accept or reject a proposed task. If she accepts the proposal, she is busy for the duration of the task and obtains a reward that depends on the task duration. If she rejects it, she remains on hold until a new task proposal arrives. We study the regret incurred by the agent, first when she knows her reward function but does not know the distribution of the task duration, and then when she does not know her reward function, either. This natural setting bears similarities with contextual (one-armed) bandits, but with the crucial difference that the normalized reward associated to a context depends on the whole distribution of contexts.

stat.ML↗

arXiv2021

Decentralized Learning in Online Queuing Systems

Motivated by packet routing in computer networks, online queuing systems are composed of queues receiving packets at different rates. Repeatedly, they send packets to servers, each of them treating only at most one packet at a time. In the centralized case, the number of accumulated packets remains bounded (i.e., the system is \textit{stable}) as long as the ratio between service rates and arrival rates is larger than $1$. In the decentralized case, individual no-regret strategies ensures stability when this ratio is larger than $2$. Yet, myopically minimizing regret disregards the long term effects due to the carryover of packets to further rounds. On the other hand, minimizing long term costs leads to stable Nash equilibria as soon as the ratio exceeds $\frac{e}{e-1}$. Stability with decentralized learning strategies with a ratio below $2$ was a major remaining question. We first argue that for ratios up to $2$, cooperation is required for stability of learning strategies, as selfish minimization of policy regret, a \textit{patient} notion of regret, might indeed still be unstable in this case. We therefore consider cooperative queues and propose the first learning decentralized algorithm guaranteeing stability of the system as long as the ratio of rates is larger than $1$, thus reaching performances comparable to centralized strategies.

stat.ML↗

arXiv2021

Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge

We consider the problem of online linear regression in the stochastic setting. We derive high probability regret bounds for online ridge regression and the forward algorithm. This enables us to compare online regression algorithms more accurately and eliminate assumptions of bounded observations and predictions. Our study advocates for the use of the forward algorithm in lieu of ridge due to its enhanced bounds and robustness to the regularization parameter. Moreover, we explain how to integrate it in algorithms involving linear function approximation to remove a boundedness assumption without deteriorating theoretical bounds. We showcase this modification in linear bandit settings where it yields improved regret bounds. Last, we provide numerical experiments to illustrate our results and endorse our intuitions.

cs.LG↗

arXiv2021

Local Differential Privacy for Regret Minimization in Reinforcement Learning

Reinforcement learning algorithms are widely used in domains where it is desirable to provide a personalized service. In these domains it is common that user data contains sensitive information that needs to be protected from third parties. Motivated by this, we study privacy in the context of finite-horizon Markov Decision Processes (MDPs) by requiring information to be obfuscated on the user side. We formulate this notion of privacy for RL by leveraging the local differential privacy (LDP) framework. We establish a lower bound for regret minimization in finite-horizon MDPs with LDP guarantees which shows that guaranteeing privacy has a multiplicative effect on the regret. This result shows that while LDP is an appealing notion of privacy, it makes the learning problem significantly more complex. Finally, we present an optimistic algorithm that simultaneously satisfies $\varepsilon$-LDP requirements, and achieves $\sqrt{K}/\varepsilon$ regret in any finite-horizon MDP after $K$ episodes, matching the lower bound dependency on the number of episodes $K$.

cs.LG↗

arXiv2021

Online Sign Identification: Minimization of the Number of Errors in Thresholding Bandits

In the fixed budget thresholding bandit problem, an algorithm sequentially allocates a budgeted number of samples to different distributions. It then predicts whether the mean of each distribution is larger or lower than a given threshold. We introduce a large family of algorithms (containing most existing relevant ones), inspired by the Frank-Wolfe algorithm, and provide a thorough yet generic analysis of their performance. This allowed us to construct new explicit algorithms, for a broad class of problems, whose losses are within a small constant factor of the non-adaptive oracle ones. Quite interestingly, we observed that adaptive methods empirically greatly out-perform non-adaptive oracles, an uncommon behavior in standard online learning settings, such as regret minimization. We explain this surprising phenomenon on an insightful toy problem.

cs.LG↗

arXiv2021

Learning in repeated auctions

Online auctions are one of the most fundamental facets of the modern economy and power an industry generating hundreds of billions of dollars a year in revenue. Auction theory has historically focused on the question of designing the best way to sell a single item to potential buyers, with the concurrent objectives of maximizing revenue generated or welfare created. Theoretical results in this area have typically relied on some prior Bayesian knowledge agents were assumed to have on each-other. This assumption is no longer satisfied in new markets such as online advertising: similar items are sold repeatedly, and agents are unaware of each other or might try to manipulate each-other. On the other hand, statistical learning theory now provides tools to supplement those missing pieces of information given enough data, as agents can learn from their environment to improve their strategies. This survey covers recent advances in learning in repeated auctions, starting from the traditional economic study of optimal one-shot auctions with a Bayesian prior. We then focus on the question of learning optimal mechanisms from a dataset of bidders' past values. The sample complexity as well as the computational efficiency of different methods will be studied. We will also investigate online variants where gathering data has a cost to be accounted for, either by seller or buyers ("earning while learning"). Later in the survey, we will further assume that bidders are also adaptive to the mechanism as they interact repeatedly with the same seller. We will show how strategic agents can actually manipulate repeated auctions, to their own advantage. All the questions discussed in this survey are grounded in real-world applications and many of the ideas and algorithms we describe are used every day to power the Internet economy.

cs.GT↗

arXiv2021

Thresholding at the monopoly price: an agnostic way to improve bidding strategies in revenue-maximizing auctions

We address the problem of improving bidders' strategies in prior-dependent revenue-maximizing auctions and introduce a simple and generic method to design novel bidding strategies if the seller uses past bids to optimize her mechanism. We propose a simple and agnostic strategy, independent of the distribution of the competition, that is robust to mechanism changes and local (as opposed to global) optimization of e.g. reserve prices by the seller. This strategy guarantees an increase in utility compared to the truthful strategy for any distribution of the competition. In textbook-style examples, for instance with uniform [0,1] value distributions and two bidders, this no-side-information and mechanism-independent strategy yields an enormous 57% increase in buyer utility for lazy second price auctions with monopoly reserves. When the bidder knows the distribution of the highest bid of the competition, we show how to optimize the tradeoff between reducing the reserve price and beating the competition. Our formulation enables to study some important robustness properties of the strategies, showing their impact even when the seller is using a data-driven approach to set the reserve prices. In this sample-size setting, we prove under what conditions, thresholding bidding strategies can still improve the buyer's utility. The gist of our approach is to see optimal auctions in practice as a Stackelberg game where the buyer is the leader, as he is the first one to move (here bid) when the seller is the follower as she has no prior information on the bidder.

cs.GT↗

arXiv2021

Pure Exploration and Regret Minimization in Matching Bandits

Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1 assumption on the adjacency matrix to reduce the sample complexity and the regret of off-the-shelf algorithms up to reaching a linear dependency in the number of vertices (up to poly log terms).

stat.ML↗

arXiv2021

Online Matching in Sparse Random Graphs: Non-Asymptotic Performances of Greedy Algorithm

Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed degree distributions -- the so-called configuration model. We estimate the competitive ratio of the simplest algorithm, GREEDY, by approximating some relevant stochastic discrete processes by their continuous counterparts, that are solutions of an explicit system of partial differential equations. This technique gives precise bounds on the estimation errors, with arbitrarily high probability as the problem size increases. In particular, it allows the formal comparison between different configuration models. We also prove that, quite surprisingly, GREEDY can have better performance guarantees than RANKING, another celebrated algorithm for online matching that usually outperforms the former.

cs.DS↗

arXiv2021

Unsupervised Neural Hidden Markov Models with a Continuous latent state space

We introduce a new procedure to neuralize unsupervised Hidden Markov Models in the continuous case. This provides higher flexibility to solve problems with underlying latent variables. This approach is evaluated on both synthetic and real data. On top of generating likely model parameters with comparable performances to off-the-shelf neural architecture (LSTMs, GRUs,..), the obtained results are easily interpretable.

cs.LG↗

arXiv2021

Offline Inverse Reinforcement Learning

The objective of offline RL is to learn optimal policies when a fixed exploratory demonstrations data-set is available and sampling additional observations is impossible (typically if this operation is either costly or rises ethical questions). In order to solve this problem, off the shelf approaches require a properly defined cost function (or its evaluation on the provided data-set), which are seldom available in practice. To circumvent this issue, a reasonable alternative is to query an expert for few optimal demonstrations in addition to the exploratory data-set. The objective is then to learn an optimal policy w.r.t. the expert's latent cost function. Current solutions either solve a behaviour cloning problem (which does not leverage the exploratory data) or a reinforced imitation learning problem (using a fixed cost function that discriminates available exploratory trajectories from expert ones). Inspired by the success of IRL techniques in achieving state of the art imitation performances in online settings, we exploit GAN based data augmentation procedures to construct the first offline IRL algorithm. The obtained policies outperformed the aforementioned solutions on multiple OpenAI gym environments.

cs.LG↗

arXiv2021

A Generalised Inverse Reinforcement Learning Framework

The gloabal objective of inverse Reinforcement Learning (IRL) is to estimate the unknown cost function of some MDP base on observed trajectories generated by (approximate) optimal policies. The classical approach consists in tuning this cost function so that associated optimal trajectories (that minimise the cumulative discounted cost, i.e. the classical RL loss) are 'similar' to the observed ones. Prior contributions focused on penalising degenerate solutions and improving algorithmic scalability. Quite orthogonally to them, we question the pertinence of characterising optimality with respect to the cumulative discounted cost as it induces an implicit bias against policies with longer mixing times. State of the art value based RL algorithms circumvent this issue by solving for the fixed point of the Bellman optimality operator, a stronger criterion that is not well defined for the inverse problem. To alleviate this bias in IRL, we introduce an alternative training loss that puts more weights on future states which yields a reformulation of the (maximum entropy) IRL problem. The algorithms we devised exhibit enhanced performances (and similar tractability) than off-the-shelf ones in multiple OpenAI gym environments.

cs.LG↗

arXiv2021

Markov Decision Process for MOOC users behavioral inference

Studies on massive open online courses (MOOCs) users discuss the existence of typical profiles and their impact on the learning process of the students. However defining the typical behaviors as well as classifying the users accordingly is a difficult task. In this paper we suggest two methods to model MOOC users behaviour given their log data. We mold their behavior into a Markov Decision Process framework. We associate the user's intentions with the MDP reward and argue that this allows us to classify them.

cs.LG↗

arXiv2021

Adversarial learning for revenue-maximizing auctions

We introduce a new numerical framework to learn optimal bidding strategies in repeated auctions when the seller uses past bids to optimize her mechanism. Crucially, we do not assume that the bidders know what optimization mechanism is used by the seller. We recover essentially all state-of-the-art analytical results for the single-item framework derived previously in the setup where the bidder knows the optimization mechanism used by the seller and extend our approach to multi-item settings, in which no optimal shading strategies were previously known. Our approach yields substantial increases in bidder utility in all settings. Our approach also has a strong potential for practical usage since it provides a simple way to optimize bidding strategies on modern marketplaces where buyers face unknown data-driven mechanisms.

cs.GT↗

arXiv2021

Be Greedy in Multi-Armed Bandits

The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known to sometimes have poor performances, for instance even a linear regret (with respect to the time horizon) in the standard multi-armed bandit problem. On the other hand, this heuristic performs reasonably well in practice and it even has sublinear, and even near-optimal, regret bounds in some very specific linear contextual and Bayesian bandit models. We build on a recent line of work and investigate bandit settings where the number of arms is relatively large and where simple greedy algorithms enjoy highly competitive performance, both in theory and in practice. We first provide a generic worst-case bound on the regret of the Greedy algorithm. When combined with some arms subsampling, we prove that it verifies near-optimal worst-case regret bounds in continuous, infinite and many-armed bandit problems. Moreover, for shorter time spans, the theoretical relative suboptimality of Greedy is even reduced. As a consequence, we subversively claim that for many interesting problems and associated horizons, the best compromise between theoretical guarantees, practical performances and computational burden is definitely to follow the greedy heuristic. We support our claim by many numerical experiments that show significant improvements compared to the state-of-the-art, even for moderately long time horizon.

cs.LG↗

arXiv2021

Statistical Efficiency of Thompson Sampling for Combinatorial Semi-Bandits

We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic with the action size) is still open for many families of distributions, including mutually independent outcomes, and more generally the multivariate sub-Gaussian family. We propose to answer the above question for these two families by analyzing variants of the Combinatorial Thompson Sampling policy (CTS). For mutually independent outcomes in $[0,1]$, we propose a tight analysis of CTS using Beta priors. We then look at the more general setting of multivariate sub-Gaussian outcomes and propose a tight analysis of CTS using Gaussian priors. This last result gives us an alternative to the Efficient Sampling for Combinatorial Bandit policy (ESCB), which, although optimal, is not computationally efficient.

stat.ML↗

arXiv2020

Online A-Optimal Design and Active Linear Regression

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate $\hatβ$ of the hidden parameter $β^{\star}$ of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of $T$ samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the $\ell^2$-loss $\mathbb{E} [\lVert\hatβ-β^{\star}\rVert^2]$ the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a $\mathcal{O}(T^{-2})$ regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings.

stat.ML↗