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We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the…
We introduce Cautious Optimism, a framework for substantially faster regularized learning in general games. Cautious Optimism, as a variant of Optimism, adaptively controls the learning pace in a dynamic, non-monotone manner to accelerate…
In this paper, we study the problem of regret minimization for episodic Reinforcement Learning (RL) both in the model-free and the model-based setting. We focus on learning with general function classes and general model classes, and we…
Much of the work in online learning focuses on the study of sublinear upper bounds on the regret. In this work, we initiate the study of best-case lower bounds in online convex optimization, wherein we bound the largest improvement an…
In this paper, we study the contextual multinomial logit (MNL) bandit problem in which a learning agent sequentially selects an assortment based on contextual information, and user feedback follows an MNL choice model. There has been a…
We study online convex optimization on $\ell_p$-balls in $\mathbb{R}^d$ for $p > 2$. While always sub-linear, the optimal regret exhibits a shift between the high-dimensional setting ($d > T$), when the dimension $d$ is greater than the…
This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer. Under…
We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret…
A large variety of real-world Reinforcement Learning (RL) tasks is characterized by a complex and heterogeneous structure that makes end-to-end (or flat) approaches hardly applicable or even infeasible. Hierarchical Reinforcement Learning…
We consider the framework of non-stationary Online Convex Optimization where a learner seeks to control its dynamic regret against an arbitrary sequence of comparators. When the loss functions are strongly convex or exp-concave, we…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
Reinforcement learning (RL) with linear function approximation has received increasing attention recently. However, existing work has focused on obtaining $\sqrt{T}$-type regret bound, where $T$ is the number of interactions with the MDP.…
We develop a novel and generic algorithm for the adversarial multi-armed bandit problem (or more generally the combinatorial semi-bandit problem). When instantiated differently, our algorithm achieves various new data-dependent regret…
We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL is important for curved losses and for understanding adaptive optimizers such as Adam, yet…
Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with $S$ states, $A$ actions and…
We provide the first sub-linear space and sub-linear regret algorithm for online learning with expert advice (against an oblivious adversary), addressing an open question raised recently by Srinivas, Woodruff, Xu and Zhou (STOC 2022). We…
We introduce the first best-of-both-worlds algorithm for contextual combinatorial semi-bandits that simultaneously guarantees $\widetilde{\mathcal{O}}(\sqrt{T})$ regret in the adversarial regime and $\widetilde{\mathcal{O}}(\ln T)$ regret…
Follow-The-Regularized-Leader (FTRL) is known as an effective and versatile approach in online learning, where appropriate choice of the learning rate is crucial for smaller regret. To this end, we formulate the problem of adjusting FTRL's…
Regret bounds in online learning compare the player's performance to $L^*$, the optimal performance in hindsight with a fixed strategy. Typically such bounds scale with the square root of the time horizon $T$. The more refined concept of…
Best-of-both-worlds algorithms for online learning which achieve near-optimal regret in both the adversarial and the stochastic regimes have received growing attention recently. Existing techniques often require careful adaptation to every…