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We present an algorithm that achieves almost optimal pseudo-regret bounds against adversarial and stochastic bandits. Against adversarial bandits the pseudo-regret is $O(K\sqrt{n \log n})$ and against stochastic bandits the pseudo-regret is…

Machine Learning · Computer Science 2016-05-30 Peter Auer , Chao-Kai Chiang

A classic problem in statistics is the estimation of the expectation of random variables from samples. This gives rise to the tightly connected problems of deriving concentration inequalities and confidence sequences, that is confidence…

Machine Learning · Statistics 2022-08-02 Francesco Orabona , Kwang-Sung Jun

We study the problem of episodic reinforcement learning in continuous state-action spaces with unknown rewards and transitions. Specifically, we consider the setting where the rewards and transitions are modeled using parametric bilinear…

Machine Learning · Computer Science 2022-10-06 Reda Ouhamma , Debabrota Basu , Odalric-Ambrym Maillard

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…

Machine Learning · Computer Science 2015-03-02 Wouter M. Koolen , Tim van Erven

Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…

Multiagent Systems · Computer Science 2021-01-08 Joseph Singleton , Richard Booth

We consider regret minimization in repeated games with non-convex loss functions. Minimizing the standard notion of regret is computationally intractable. Thus, we define a natural notion of regret which permits efficient optimization and…

Machine Learning · Computer Science 2017-11-06 Elad Hazan , Karan Singh , Cyril Zhang

The success of lexicase selection has led to various extensions, including its combination with down-sampling, which further increased performance. However, recent work found that down-sampling also leads to significant improvements in the…

Neural and Evolutionary Computing · Computer Science 2025-02-26 Alina Geiger , Martin Briesch , Dominik Sobania , Franz Rothlauf

We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory…

Machine Learning · Computer Science 2023-01-31 Uri Sherman , Tomer Koren , Yishay Mansour

Sequential design of experiments for optimizing a reward function in causal systems can be effectively modeled by the sequential design of interventions in causal bandits (CBs). In the existing literature on CBs, a critical assumption is…

Machine Learning · Statistics 2024-03-06 Zirui Yan , Arpan Mukherjee , Burak Varıcı , Ali Tajer

Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions…

Machine Learning · Computer Science 2025-08-11 Víctor Bucarey , Sophia Calderón , Gonzalo Muñoz , Frederic Semet

We study the fundamental problem of prediction with expert advice and develop regret lower bounds for a large family of algorithms for this problem. We develop simple adversarial primitives, that lend themselves to various combinations…

Machine Learning · Computer Science 2016-07-15 Nick Gravin , Yuval Peres , Balasubramanian Sivan

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)…

Computer Science and Game Theory · Computer Science 2021-03-09 Gabriele Farina , Tuomas Sandholm

Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1…

Machine Learning · Statistics 2021-08-03 Flore Sentenac , Jialin Yi , Clément Calauzènes , Vianney Perchet , Milan Vojnovic

We study how the regret guarantees of nonstochastic multi-armed bandits can be improved, if the effective range of the losses in each round is small (e.g. the maximal difference between two losses in a given round). Despite a recent…

Machine Learning · Computer Science 2020-01-03 Nicolò Cesa-Bianchi , Ohad Shamir

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…

Machine Learning · Computer Science 2026-05-12 Tingkai Jia , Haiguang Wang , Cheng Chen

By incorporating regret minimization, double oracle methods have demonstrated rapid convergence to Nash Equilibrium (NE) in normal-form games and extensive-form games, through algorithms such as online double oracle (ODO) and extensive-form…

Computer Science and Game Theory · Computer Science 2023-07-14 Xiaohang Tang , Le Cong Dinh , Stephen Marcus McAleer , Yaodong Yang

The problem of variable clustering is that of grouping similar components of a $p$-dimensional vector $X=(X_{1},\ldots,X_{p})$, and estimating these groups from $n$ independent copies of $X$. When cluster similarity is defined via…

Statistics Theory · Mathematics 2016-06-17 Florentina Bunea , Christophe Giraud , Martin Royer , Nicolas Verzelen

The break minimization problem is a fundamental problem in sports scheduling. Recently, its quadratic unconstrained binary optimization (QUBO) formulation has been proposed, which has gained much interest with the rapidly growing field of…

Discrete Mathematics · Computer Science 2023-07-04 Koichi Fujii , Tomomi Matsui

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…

Machine Learning · Computer Science 2025-12-16 Soumita Hait , Ping Li , Haipeng Luo , Mengxiao Zhang

Bilateral trade is a central problem in algorithmic economics, and recent work has explored how to design trading mechanisms using no-regret learning algorithms. However, no-regret learning is impossible when budget balance has to be…

Computer Science and Game Theory · Computer Science 2025-07-16 Anna Lunghi , Matteo Castiglioni , Alberto Marchesi