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  1. arXiv:2402.05300v2 (Ed.)
    This paper considers a multi-player resource-sharing game with a fair reward allocation model. Multiple players choose from a collection of resources. Each resource brings a random reward equally divided among the players who choose it. We consider two settings. The first setting is a one-slot game where the mean rewards of the resources are known to all the players, and the objective of player 1 is to maximize their worst-case expected utility. Certain special cases of this setting have explicit solutions. These cases provide interesting yet non-intuitive insights into the problem. The second setting is an online setting, where the game is played over a finite time horizon, where the mean rewards are unknown to the first player. Instead, the first player receives, as feedback, the rewards of the resources they chose after the action. We develop a novel Upper Confidence Bound (UCB) algorithm that minimizes the worst-case regret of the first player using the feedback received. 
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    Free, publicly-accessible full text available March 4, 2025
  2. arXiv:2401.07170v1 (Ed.)
    This paper considers online optimization for a system that performs a sequence of back-to-back tasks. Each task can be processed in one of multiple processing modes that affect the duration of the task, the reward earned, and an additional vector of penalties (such as energy or cost). Let A[k] be a random matrix of parameters that specifies the duration, reward, and penalty vector under each processing option for task k. The goal is to observe A[k] at the start of each new task k and then choose a processing mode for the task so that, over time, time average reward is maximized subject to time average penalty constraints. This is a renewal optimization problem and is challenging because the probability distribution for the A[k] sequence is unknown. Prior work shows that any algorithm that comes within ϵ of optimality must have (1/ϵ^2) convergence time. The only known algorithm that can meet this bound operates without time average penalty constraints and uses a diminishing stepsize that cannot adapt when probabilities change. This paper develops a new algorithm that is adaptive and comes within O(ϵ) of optimality for any interval of  (1/ϵ^2) tasks over which probabilities are held fixed, regardless of probabilities before the start of the interval. 
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    Free, publicly-accessible full text available January 13, 2025
  3. arXiv:2311.11180v1 (Ed.)
    This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank-Wolfe algorithm and its variants already avoid projections, they are primarily designed for smooth objective functions. In con- trast, our proposed algorithm can handle nonsmooth problems with general convex functional inequality constraints. It achieves an ϵ-suboptimal solution in O(ϵ^−2) iterations, with each iteration requiring only a single (potentially inexact) Linear Minimization Oracle (LMO) call and a (possibly inexact) subgra- dient computation. This performance is consistent with existing lower bounds. Similar performance is observed when deterministic subgradients are replaced with stochastic subgradients. In the special case where there are no functional inequality constraints, our algorithm competes favorably with a recent nonsmooth projection-free method designed for constraint-free problems. Our approach uti- lizes a simple separation scheme in conjunction with a new Lagrange multiplier update rule. 
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    Free, publicly-accessible full text available November 18, 2024