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We study a variant of online convex optimization where the player is permitted to switch decisions at most $S$ times in expectation throughout $T$ rounds. Similar problems have been addressed in prior work for the discrete decision set…
We revisit the classic online portfolio selection problem, where at each round a learner selects a distribution over a set of portfolios to allocate its wealth. It is known that for this problem a logarithmic regret with respect to Cover's…
We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total…
We study online convex optimization with constraints consisting of multiple functional constraints and a relatively simple constraint set, such as a Euclidean ball. As enforcing the constraints at each time step through projections is…
This paper presents a new framework for analyzing and designing no-regret algorithms for dynamic (possibly adversarial) systems. The proposed framework generalizes the popular online convex optimization framework and extends it to its…
We study an algorithmic equivalence technique between non-convex gradient descent and convex mirror descent. We start by looking at a harder problem of regret minimization in online non-convex optimization. We show that under certain…
We consider the problem of minimizing different notions of swap regret in online optimization. These forms of regret are tightly connected to correlated equilibrium concepts in games, and have been more recently shown to guarantee…
Pairwise learning is essential in machine learning, especially for problems involving loss functions defined on pairs of training examples. Online gradient descent (OGD) algorithms have been proposed to handle online pairwise learning,…
Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…
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…
Although online convex optimization (OCO) under arbitrary delays has received increasing attention recently, previous studies focus on stationary environments with the goal of minimizing static regret. In this paper, we investigate the…
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…
In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm,…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the $G^\star$ regret, depends on the cumulative squared gradient norm evaluated at the decision in…
We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the…
We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in…
We consider online learning problems in the realizable setting, where there is a zero-loss solution, and propose new Differentially Private (DP) algorithms that obtain near-optimal regret bounds. For the problem of online prediction from…
We give a randomized online algorithm that guarantees near-optimal $\widetilde O(\sqrt T)$ expected swap regret against any sequence of $T$ adaptively chosen Lipschitz convex losses on the unit interval. This improves the previous best…
We show that Optimistic Hedge -- a common variant of multiplicative-weights-updates with recency bias -- attains ${\rm poly}(\log T)$ regret in multi-player general-sum games. In particular, when every player of the game uses Optimistic…