Related papers: Infinite-Dimensional Operator/Block Kaczmarz Algor…
We consider the dynamic resource allocation problem where the decision space is finite-dimensional, yet the solution must satisfy a large or even infinite number of constraints revealed via streaming data or oracle feedback. We model this…
We develop a new approach to obtaining high probability regret bounds for online learning with bandit feedback against an adaptive adversary. While existing approaches all require carefully constructing optimistic and biased loss…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
Motivated by applications to online learning in sparse estimation and Bayesian optimization, we consider the problem of online unconstrained nonsubmodular minimization with delayed costs in both full information and bandit feedback…
Recent advances in Reinforcement Learning from Human Feedback (RLHF) have shown that KL-regularization plays a pivotal role in improving the efficiency of RL fine-tuning for large language models (LLMs). Despite its empirical advantage, the…
This work focuses on the setting of dynamic regret in the context of online learning with full information. In particular, we analyze regret bounds with respect to the temporal variability of the loss functions. By assuming that the…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
We study the adversarial kernel bandit problem, in which the loss at each round is induced by an arbitrary bounded element of a reproducing kernel Hilbert space (RKHS). We propose an exponential-weights algorithm built on a regularized…
We consider a generalization of the celebrated Online Convex Optimization (OCO) framework with adversarial online constraints. In this problem, an online learner interacts with an adversary sequentially over multiple rounds. At the…
We study the problem of reinforcement learning in infinite-horizon discounted linear Markov decision processes (MDPs), and propose the first computationally efficient algorithm achieving rate-optimal regret guarantees in this setting. Our…
We study linear bandits when the underlying reward function is not linear. Existing work relies on a uniform misspecification parameter $\epsilon$ that measures the sup-norm error of the best linear approximation. This results in an…
We provide improved gap-dependent regret bounds for reinforcement learning in finite episodic Markov decision processes. Compared to prior work, our bounds depend on alternative definitions of gaps. These definitions are based on the…
This paper studies online optimization from a high-level unified theoretical perspective. We not only generalize both Optimistic-DA and Optimistic-MD in normed vector space, but also unify their analysis methods for dynamic regret. Regret…
We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances. We prove the first finite-time regret bounds for adaptive nonlinear control with matched uncertainty in the stochastic…
Online bilevel optimization (OBO) has emerged as a powerful framework for many machine learning problems. Prior works have developed several algorithms that minimize the standard bilevel local regret or the window-averaged bilevel local…
To conduct a more in-depth investigation of randomized solvers for solving linear systems, we adopt a unified randomized batch-sampling Kaczmarz framework with per-iteration costs as low as cyclic block methods, and develop a general…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
We consider stochastic multi-armed bandit problems where the expected reward is a Lipschitz function of the arm, and where the set of arms is either discrete or continuous. For discrete Lipschitz bandits, we derive asymptotic problem…
We develop the first parameter-free algorithms for the Stochastically Extended Adversarial (SEA) model, a framework that bridges adversarial and stochastic online convex optimization. Existing approaches for the SEA model require prior…
This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and…