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We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain "sufficient statistics" for the data sequence, then there exists a special Burkholder function that 1) can be used…
A crucial problem in reinforcement learning is learning the optimal policy. We study this in tabular infinite-horizon discounted Markov decision processes under the online setting. The existing algorithms either fail to achieve regret…
Given any increasing sequence of norms $\|\cdot\|_0,\dots,\|\cdot\|_{T-1}$, we provide an online convex optimization algorithm that outputs points $w_t$ in some domain $W$ in response to convex losses $\ell_t:W\to \mathbb{R}$ that…
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…
Multitask learning is a powerful framework that enables one to simultaneously learn multiple related tasks by sharing information between them. Quantifying uncertainty in the estimated tasks is of pivotal importance for many downstream…
This paper examines whether widely used online learning algorithms in pricing can independently reach competitive outcomes or instead foster tacit collusion. This issue has drawn considerable attention from competition regulators as…
In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called…
We study the problem of non-constrained, discrete-time, online distributed optimization in a multi-agent system where some of the agents do not follow the prescribed update rule either due to failures or malicious intentions. None of the…
Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance…
Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic…
We provide algorithms that guarantee regret $R_T(u)\le \tilde O(G\|u\|^3 + G(\|u\|+1)\sqrt{T})$ or $R_T(u)\le \tilde O(G\|u\|^3T^{1/3} + GT^{1/3}+ G\|u\|\sqrt{T})$ for online convex optimization with $G$-Lipschitz losses for any comparison…
We study the framework of universal dynamic regret minimization with strongly convex losses. We answer an open problem in Baby and Wang 2021 by showing that in a proper learning setup, Strongly Adaptive algorithms can achieve the near…
Researchers have demonstrated that neural networks are vulnerable to adversarial examples and subtle environment changes, both of which one can view as a form of distribution shift. To humans, the resulting errors can look like blunders,…
We consider the problem of decentralized multi-agent reinforcement learning in Markov games. A fundamental question is whether there exist algorithms that, when adopted by all agents and run independently in a decentralized fashion, lead to…
In this paper, we study adaptive online convex optimization, and aim to design a universal algorithm that achieves optimal regret bounds for multiple common types of loss functions. Existing universal methods are limited in the sense that…
Algorithmic \emph{replicability} has recently been introduced to address the need for reproducible experiments in machine learning. A \emph{replicable online learning} algorithm is one that takes the same sequence of decisions across…
The proliferation of the Internet has led to the emergence of online advertising, driven by the mechanics of online auctions. In these repeated auctions, software agents participate on behalf of aggregated advertisers to optimize for their…
In the online learning with experts problem, an algorithm must make a prediction about an outcome on each of $T$ days (or times), given a set of $n$ experts who make predictions on each day (or time). The algorithm is given feedback on the…
In online advertising markets, budget-constrained advertisers acquire ad placements through repeated bidding in auctions on various platforms. We present a strategy for bidding optimally in a set of auctions that may or may not be…
We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as $\sqrt{T}$ unless strong stochastic assumptions are imposed on the…