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We study a class of adversarial bandit optimization problems in which the loss functions may be non-convex and non-smooth. In each round, the learner observes a loss that consists of an underlying linear component together with an…
We study the problem of global optimization, where we analyze the performance of the Piyavskii--Shubert algorithm and its variants. For any given time duration $T$, instead of the extensively studied simple regret (which is the difference…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
We study online learning with oblivious losses and delays under a novel ``capacity constraint'' that limits how many past rounds can be tracked simultaneously for delayed feedback. Under ``clairvoyance'' (i.e., delay durations are revealed…
Most learning algorithms with formal regret guarantees assume that all mistakes are recoverable and essentially rely on trying all possible behaviors. This approach is problematic when some mistakes are "catastrophic", i.e., irreparable. We…
Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR)…
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 aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision…
We study dynamic pricing where a seller repeatedly interacts with a strategic, non-myopic buyer who has a fixed private valuation and discounts future utility. Prior work focused exclusively on posted-price mechanisms, which only extract…
Optimization models used to make discrete decisions often contain uncertain parameters that are context-dependent and estimated through prediction. To account for the quality of the decision made based on the prediction, decision-focused…
In this paper we study the non-stationary stochastic optimization question with bandit feedback and dynamic regret measures. The seminal work of Besbes et al. (2015) shows that, when aggregated function changes is known a priori, a simple…
We revisit the study of optimal regret rates in bandit combinatorial optimization---a fundamental framework for sequential decision making under uncertainty that abstracts numerous combinatorial prediction problems. We prove that the…
This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…
Policy design in non-stationary Markov Decision Processes (MDPs) is inherently challenging due to the complexities introduced by time-varying system transition and reward, which make it difficult for learners to determine the optimal…
We consider the problem of online linear regression on individual sequences. The goal in this paper is for the forecaster to output sequential predictions which are, after $T$ time rounds, almost as good as the ones output by the best…
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…
We study contextual dynamic pricing under a semiparametric demand model in which the purchase probability is $1-F(p-m(\mathbf{x}))$, where $m(\mathbf{x})$ captures mean utility as a function of product features and buyer covariates, and $F$…
Online learning and model reference adaptive control have many interesting intersections. One area where they differ however is in how the algorithms are analyzed and what objective or metric is used to discriminate "good" algorithms from…
We study the optimal trade-off between expectation and tail risk for regret distribution in the stochastic multi-armed bandit model. We fully characterize the interplay among three desired properties for policy design: worst-case…
We introduce efficient algorithms which achieve nearly optimal regrets for the problem of stochastic online shortest path routing with end-to-end feedback. The setting is a natural application of the combinatorial stochastic bandits…