Related papers: A double oracle approach for minmax regret optimiz…
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
We study the $K$-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. We introduce a tight asymptotic regret lower bound that is based…
Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are…
We study the problem of determining an effective exploration strategy in static and non-linear optimization problems, which depend on an unknown scalar parameter to be learned from online collected noisy data. An optimal trade-off between…
We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second…
We study the combinatorial semi-bandit problem under matroid constraints. The regret achieved by recent approaches is optimal, in the sense that it matches the lower bound. Yet, time complexity remains an issue for large matroids or for…
In this work, we investigate black-box optimization from the perspective of frequentist kernel methods. We propose a novel batch optimization algorithm, which jointly maximizes the acquisition function and select points from a whole batch…
We introduce the dual-path fixing strategy to exploit dual algorithms for solving relaxations of mixed-integer nonlinear-optimization problems. Such dual algorithms are naturally applied in the context of branch-and-bound, and eventual…
We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…
In this paper, we study a class of online optimization problems with long-term budget constraints where the objective functions are not necessarily concave (nor convex) but they instead satisfy the Diminishing Returns (DR) property.…
Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds…
Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and…
We study Online Linear Programming (OLP) with batching. The planning horizon is cut into $K$ batches, and the decisions on customers arriving within a batch can be delayed to the end of their associated batch. Compared with OLP without…
The framework of online learning with memory naturally captures learning problems with temporal constraints, and was previously studied for the experts setting. In this work we extend the notion of learning with memory to the general Online…
We study regret minimization in non-episodic factored Markov decision processes (FMDPs), where all existing algorithms make the strong assumption that the factored structure of the FMDP is known to the learner in advance. In this paper, we…
Bilevel optimization problems arise in many applications where decisions must account for the optimal response of another system, such as in game-theoretic settings. However, these problems are notoriously challenging, as even linear…
In this paper, we investigate the existence of online learning algorithms with bandit feedback that simultaneously guarantee $O(1)$ regret compared to a given comparator strategy, and $\tilde{O}(\sqrt{T})$ regret compared to any fixed…
The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence ($V_T$) and/or the path-length of the minimizer sequence after $T$ rounds. For strongly convex and smooth…
This paper studies the problem of online performance optimization of constrained closed-loop control systems, where both the objective and the constraints are unknown black-box functions affected by exogenous time-varying contextual…
In this paper we study two-player bilinear zero-sum games with constrained strategy spaces. An instance of natural occurrences of such constraints is when mixed strategies are used, which correspond to a probability simplex constraint. We…