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A well-studied generalization of the standard online convex optimization (OCO) framework is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the…
This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In…
Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
Regret matching (RM) -- and its modern variants -- is a foundational online algorithm that has been at the heart of many AI breakthrough results in solving benchmark zero-sum games, such as poker. Yet, surprisingly little is known so far in…
We study the problem of online learning in predictive control of an unknown linear dynamical system with time varying cost functions which are unknown apriori. Specifically, we study the online learning problem where the control algorithm…
Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point…
Robust Ordinal Regression (ROR) is a way of dealing with Multiple Criteria Decision Aiding (MCDA), by considering all sets of parameters of an assumed preference model, that are compatible with preference information given by the Decision…
Distributionally Robust Optimization (DRO) is a worst-case approach to decision making when there is model uncertainty. It is also well known that for certain uncertainty sets, DRO is approximated by a regularized nominal problem. We show…
Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where…
We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret…
We consider the setting of online logistic regression and consider the regret with respect to the 2-ball of radius B. It is known (see [Hazan et al., 2014]) that any proper algorithm which has logarithmic regret in the number of samples…
Group Relative Policy Optimization (GRPO) enhances LLM reasoning but often induces overconfidence, where incorrect responses yield lower perplexity than correct ones, degrading relative calibration as described by the Area Under the Curve…
We revisit the problem of online learning with sleeping experts/bandits: in each time step, only a subset of the actions are available for the algorithm to choose from (and learn about). The work of Kleinberg et al. (2010) showed that there…
In many operational settings, decision-makers must commit to actions before uncertainty resolves, but existing optimization tools rarely quantify how consistently a chosen decision remains optimal across plausible scenarios. This paper…
We consider the online convex optimization problem. In the setting of arbitrary sequences and finite set of parameters, we establish a new fast-rate quantile regret bound. Then we investigate the optimization into the L1-ball by…
Motivated by alternating learning dynamics in two-player games, a recent work by Cevher et al.(2024) shows that $o(\sqrt{T})$ alternating regret is possible for any $T$-round adversarial Online Linear Optimization (OLO) problem, and left as…
We consider the problem of decision-making under uncertainty in an environment with safety constraints. Many business and industrial applications rely on real-time optimization to improve key performance indicators. In the case of unknown…
We consider the problem of online learning where the sequence of actions played by the learner must adhere to an unknown safety constraint at every round. The goal is to minimize regret with respect to the best safe action in hindsight…
In adversarial multi-armed bandits, two performance measures are commonly used: static regret, which compares the learner to the best fixed arm, and dynamic regret, which compares it to the best sequence of arms. While optimal algorithms…