Related papers: Tight Lower Bounds for Multiplicative Weights Algo…

We study the problem of online clustering where a clustering algorithm has to assign a new point that arrives to one of $k$ clusters. The specific formulation we use is the $k$-means objective: At each time step the algorithm has to…

This paper presents new \emph{variance-aware} confidence sets for linear bandits and linear mixture Markov Decision Processes (MDPs). With the new confidence sets, we obtain the follow regret bounds: For linear bandits, we obtain an…

We study the problem of infinite-horizon average-reward reinforcement learning with linear Markov decision processes (MDPs). The associated Bellman operator of the problem not being a contraction makes the algorithm design challenging.…

The expected regret of any reinforcement learning algorithm is lower bounded by $\Omega\left(\sqrt{DXAT}\right)$ for undiscounted returns, where $D$ is the diameter of the Markov decision process, $X$ the size of the state space, $A$ the…

In the classic expert problem, $\Phi$-regret measures the gap between the learner's total loss and that achieved by applying the best action transformation $\phi \in \Phi$. A recent work by Lu et al., [2025] introduces an adaptive algorithm…

We study the Thompson sampling algorithm in an adversarial setting, specifically, for adversarial bit prediction. We characterize the bit sequences with the smallest and largest expected regret. Among sequences of length $T$ with $k <…

We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we…

The problem of multi-armed bandits (MAB) asks to make sequential decisions while balancing between exploitation and exploration, and have been successfully applied to a wide range of practical scenarios. Various algorithms have been…

Policy optimization methods are popular reinforcement learning algorithms in practice. Recent works have built theoretical foundation for them by proving $\sqrt{T}$ regret bounds even when the losses are adversarial. Such bounds are tight…

We tackle the problem of online optimization with a general, possibly unbounded, loss function. It is well known that when the loss is bounded, the exponentially weighted aggregation strategy (EWA) leads to a regret in $\sqrt{T}$ after $T$…

We consider the classical problem of sequential probability assignment under logarithmic loss while competing against an arbitrary, potentially nonparametric class of experts. We obtain tight bounds on the minimax regret via a new approach…

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…

In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic…

In a low-rank linear bandit problem, the reward of an action (represented by a matrix of size $d_1 \times d_2$) is the inner product between the action and an unknown low-rank matrix $\Theta^*$. We propose an algorithm based on a novel…

We give improved tradeoffs between space and regret for the online learning with expert advice problem over $T$ days with $n$ experts. Given a space budget of $n^{\delta}$ for $\delta \in (0,1)$, we provide an algorithm achieving regret…

We revisit the classic regret-minimization problem in the stochastic multi-armed bandit setting when the arm-distributions are allowed to be heavy-tailed. Regret minimization has been well studied in simpler settings of either bounded…

In online learning problems, exploiting low variance plays an important role in obtaining tight performance guarantees yet is challenging because variances are often not known a priori. Recently, considerable progress has been made by Zhang…

Performance of adaptive control policies is assessed through the regret with respect to the optimal regulator, which reflects the increase in the operating cost due to uncertainty about the dynamics parameters. However, available results in…

We consider the adversarial multi-armed bandit problem under delayed feedback. We analyze variants of the Exp3 algorithm that tune their step-size using only information (about the losses and delays) available at the time of the decisions,…

We initiate the study of learning in contextual bandits with the help of loss predictors. The main question we address is whether one can improve over the minimax regret $\mathcal{O}(\sqrt{T})$ for learning over $T$ rounds, when the total…