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Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report…
The framework of online learning with memory naturally captures learning problems with temporal constraints, and was previously studied for the experts setting. In this work we extend the notion of learning with memory to the general Online…
This paper proposes a linear bandit algorithm that is adaptive to environments at two different levels of hierarchy. At the higher level, the proposed algorithm adapts to a variety of types of environments. More precisely, it achieves…
In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $O(HS\sqrt{AT})$ in the infinite-horizon zero-sum…
In this paper, we improve the regret bound for online kernel selection under bandit feedback. Previous algorithm enjoys a $O((\Vert f\Vert^2_{\mathcal{H}_i}+1)K^{\frac{1}{3}}T^{\frac{2}{3}})$ expected bound for Lipschitz loss functions. We…
We study reinforcement learning in stochastic path (SP) problems. The goal in these problems is to maximize the expected sum of rewards until the agent reaches a terminal state. We provide the first regret guarantees in this general problem…
This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret…
This paper describes a new parameter-free online learning algorithm for changing environments. In comparing against algorithms with the same time complexity as ours, we obtain a strongly adaptive regret bound that is a factor of at least…
We study the constrained variant of the \emph{multi-armed bandit} (MAB) problem, in which the learner aims not only at minimizing the total loss incurred during the learning dynamic, but also at controlling the violation of multiple…
One of the primary challenges in large-scale distributed learning stems from stringent communication constraints. While several recent works address this challenge for static optimization problems, sequential decision-making under…
Stochastic linear bandits are a fundamental model for sequential decision making, where an agent selects a vector-valued action and receives a noisy reward with expected value given by an unknown linear function. Although well studied in…
We study the problem of dynamic regret minimization in online convex optimization, in which the objective is to minimize the difference between the cumulative loss of an algorithm and that of an arbitrary sequence of comparators. While the…
We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can…
We provide algorithms that guarantee regret $R_T(u)\le \tilde O(G\|u\|^3 + G(\|u\|+1)\sqrt{T})$ or $R_T(u)\le \tilde O(G\|u\|^3T^{1/3} + GT^{1/3}+ G\|u\|\sqrt{T})$ for online convex optimization with $G$-Lipschitz losses for any comparison…
One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that…
We study the problem of non-stationary dueling bandits and provide the first adaptive dynamic regret algorithm for this problem. The only two existing attempts in this line of work fall short across multiple dimensions, including…
We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…
We study online linear optimization with matrix variables constrained by the operator norm, a setting where the geometry renders designing data-dependent and efficient adaptive algorithms challenging. The best-known adaptive regret bounds…
We study fast rates of convergence in the setting of nonparametric online regression, namely where regret is defined with respect to an arbitrary function class which has bounded complexity. Our contributions are two-fold: - In the…
In this work, we develop linear bandit algorithms that automatically adapt to different environments. By plugging a novel loss estimator into the optimization problem that characterizes the instance-optimal strategy, our first algorithm not…