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Bandits 1

Moderator: Romain Camilleri


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Wed 21 July 7:00 - 7:20 PDT

High-dimensional Experimental Design and Kernel Bandits

Romain Camilleri · Kevin Jamieson · Julian Katz-Samuels

In recent years methods from optimal linear experimental design have been leveraged to obtain state of the art results for linear bandits. A design returned from an objective such as G-optimal design is actually a probability distribution over a pool of potential measurement vectors. Consequently, one nuisance of the approach is the task of converting this continuous probability distribution into a discrete assignment of N measurements. While sophisticated rounding techniques have been proposed, in d dimensions they require N to be at least d, d log(log(d)), or d^2 based on the sub-optimality of the solution. In this paper we are interested in settings where N may be much less than d, such as in experimental design in an RKHS where d may be effectively infinite.
In this work, we propose a rounding procedure that frees N of any dependence on the dimension d, while achieving nearly the same performance guarantees of existing rounding procedures. We evaluate the procedure against a baseline that projects the problem to a lower dimensional space and performs rounding there, which requires N to just be at least a notion of the effective dimension. We also leverage our new approach in a new algorithm for kernelized bandits to obtain state of the art results for regret minimization and pure exploration. An advantage of our approach over existing UCB-like approaches is that our kernel bandit algorithms are provably robust to model misspecification.

Wed 21 July 7:20 - 7:25 PDT

Dichotomous Optimistic Search to Quantify Human Perception

Julien Audiffren

In this paper we address a variant of the continuous multi-armed bandits problem, called the threshold estimation problem, which is at the heart of many psychometric experiments. Here, the objective is to estimate the sensitivity threshold for an unknown psychometric function Psi, which is assumed to be non decreasing and continuous. Our algorithm, Dichotomous Optimistic Search (DOS), efficiently solves this task by taking inspiration from hierarchical multi-armed bandits and Black-box optimization. Compared to previous approaches, DOS is model free and only makes minimal assumption on Psi smoothness, while having strong theoretical guarantees that compares favorably to recent methods from both Psychophysics and Global Optimization. We also empirically evaluate DOS and show that it significantly outperforms these methods, both in experiments that mimics the conduct of a psychometric experiment, and in tests with large pulls budgets that illustrate the faster convergence rate.

Wed 21 July 7:25 - 7:30 PDT

Improved Confidence Bounds for the Linear Logistic Model and Applications to Bandits

Kwang-Sung Jun · Lalit Jain · Blake Mason · Houssam Nassif

We propose improved fixed-design confidence bounds for the linear logistic model. Our bounds significantly improve upon the state-of-the-art bound by Li et al. (2017) via recent developments of the self-concordant analysis of the logistic loss (Faury et al., 2020). Specifically, our confidence bound avoids a direct dependence on $1/\kappa$, where $\kappa$ is the minimal variance over all arms' reward distributions. In general, $1/\kappa$ scales exponentially with the norm of the unknown linear parameter $\theta^*$. Instead of relying on this worst case quantity, our confidence bound for the reward of any given arm depends directly on the variance of that arm's reward distribution. We present two applications of our novel bounds to pure exploration and regret minimization logistic bandits improving upon state-of-the-art performance guarantees. For pure exploration we also provide a lower bound highlighting a dependence on $1/\kappa$ for a family of instances.

Wed 21 July 7:30 - 7:35 PDT

Stochastic Multi-Armed Bandits with Unrestricted Delay Distributions

Tal Lancewicki · Shahar Segal · Tomer Koren · Yishay Mansour

We study the stochastic Multi-Armed Bandit~(MAB) problem with random delays in the feedback received by the algorithm. We consider two settings: the {\it reward dependent} delay setting, where realized delays may depend on the stochastic rewards, and the {\it reward-independent} delay setting. Our main contribution is algorithms that achieve near-optimal regret in each of the settings, with an additional additive dependence on the quantiles of the delay distribution. Our results do not make any assumptions on the delay distributions: in particular, we do not assume they come from any parametric family of distributions and allow for unbounded support and expectation; we further allow for the case of infinite delays where the algorithm might occasionally not observe any feedback.

Wed 21 July 7:35 - 7:40 PDT

Deciding What to Learn: A Rate-Distortion Approach

Dilip Arumugam · Benjamin Van Roy

Agents that learn to select optimal actions represent a prominent focus of the sequential decision-making literature. In the face of a complex environment or constraints on time and resources, however, aiming to synthesize such an optimal policy can become infeasible. These scenarios give rise to an important trade-off between the information an agent must acquire to learn and the sub-optimality of the resulting policy. While an agent designer has a preference for how this trade-off is resolved, existing approaches further require that the designer translate these preferences into a fixed learning target for the agent. In this work, leveraging rate-distortion theory, we automate this process such that the designer need only express their preferences via a single hyperparameter and the agent is endowed with the ability to compute its own learning targets that best achieve the desired trade-off. We establish a general bound on expected discounted regret for an agent that decides what to learn in this manner along with computational experiments that illustrate the expressiveness of designer preferences and even show improvements over Thompson sampling in identifying an optimal policy.

Wed 21 July 7:40 - 7:45 PDT

No-regret Algorithms for Capturing Events in Poisson Point Processes

Mojmir Mutny · Andreas Krause

Inhomogeneous Poisson point processes are widely used  models of event occurrences. We address \emph{adaptive sensing of Poisson Point processes}, namely, maximizing the number of captured events subject to sensing costs. We encode prior assumptions on the rate function by modeling it as a member of a known \emph{reproducing kernel Hilbert space} (RKHS). By partitioning the domain into separate small regions, and using heteroscedastic linear regression, we propose a tractable estimator of Poisson process rates for two feedback models: \emph{count-record}, where exact locations of events are observed, and \emph{histogram} feedback, where only counts of events are observed. We derive provably accurate anytime confidence estimates for our estimators for sequentially acquired Poisson count data. Using these, we formulate algorithms based on optimism that provably incur sublinear count-regret. We demonstrate the practicality of the method on problems from crime modeling, revenue maximization as well as environmental monitoring.

Wed 21 July 7:45 - 7:50 PDT

Parametric Graph for Unimodal Ranking Bandit

Camille-Sovanneary GAUTHIER · Romaric Gaudel · Elisa Fromont · Boammani Aser Lompo

We tackle the online ranking problem of assigning $L$ items to $K$ positions on a web page in order to maximize the number of user clicks. We propose an original algorithm, easy to implement and with strong theoretical guarantees to tackle this problem in the Position-Based Model (PBM) setting, well suited for applications where items are displayed on a grid. Besides learning to rank, our algorithm, GRAB (for parametric Graph for unimodal RAnking Bandit), also learns the parameter of a compact graph over permutations of $K$ items among $L$. The logarithmic regret bound of this algorithm is a direct consequence of the unimodality property of the bandit setting with respect to the learned graph. Experiments against state-of-the-art learning algorithms which also tackle the PBM setting, show that our method is more efficient while giving regret performance on par with the best known algorithms on simulated and real life datasets.

Wed 21 July 7:50 - 7:55 PDT