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With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…

We consider the problem of controlling an unknown linear quadratic Gaussian (LQG) system consisting of multiple subsystems connected over a network. Our goal is to minimize and quantify the regret (i.e. loss in performance) of our strategy…

We consider the problem of adaptive Model Predictive Control (MPC) for uncertain linear-systems with additive disturbances and with state and input constraints. We present STT-MPC (Self-Tuning Tube-based Model Predictive Control), an online…

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…

Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by 1/{\sigma} with…

Any reinforcement learning algorithm that applies to all Markov decision processes (MDPs) will suffer $\Omega(\sqrt{SAT})$ regret on some MDP, where $T$ is the elapsed time and $S$ and $A$ are the cardinalities of the state and action…

In this paper we propose a novel experimental design-based algorithm to minimize regret in online stochastic linear and combinatorial bandits. While existing literature tends to focus on optimism-based algorithms--which have been shown to…

Understanding how to efficiently learn while adhering to safety constraints is essential for using online reinforcement learning in practical applications. However, proving rigorous regret bounds for safety-constrained reinforcement…

We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety…

The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding…

In this paper, we revisit the problem of smoothed online learning, in which the online learner suffers both a hitting cost and a switching cost, and target two performance metrics: competitive ratio and dynamic regret with switching cost.…

This paper studies the stochastic linear bandit problem, where a decision-maker chooses actions from possibly time-dependent sets of vectors in $\mathbb{R}^d$ and receives noisy rewards. The objective is to minimize regret, the difference…

We study time-inhomogeneous episodic reinforcement learning (RL) under general function approximation and sparse rewards. We design a new algorithm, Variance-weighted Optimistic $Q$-Learning (VO$Q$L), based on $Q$-learning and bound its…

We give a randomized online algorithm that guarantees near-optimal $\widetilde O(\sqrt T)$ expected swap regret against any sequence of $T$ adaptively chosen Lipschitz convex losses on the unit interval. This improves the previous best…

In recent years, significant attention has been directed towards learning average-reward Markov Decision Processes (MDPs). However, existing algorithms either suffer from sub-optimal regret guarantees or computational inefficiencies. In…

This work studies the problem of learning episodic Markov Decision Processes with known transition and bandit feedback. We develop the first algorithm with a ``best-of-both-worlds'' guarantee: it achieves $\mathcal{O}(log T)$ regret when…

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…

Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making. While such bounds…

Safety in reinforcement learning has become increasingly important in recent years. Yet, existing solutions either fail to strictly avoid choosing unsafe actions, which may lead to catastrophic results in safety-critical systems, or fail to…

We derive an alternative proof for the regret of Thompson sampling (\ts) in the stochastic linear bandit setting. While we obtain a regret bound of order $\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof sheds new light on…