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We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption. By relating the method's rate of convergence to an initial outer approximation's…
The alternating direction method of multipliers (ADMM) is a most widely used optimization scheme for solving linearly constrained separable convex optimization problems. The convergence of the ADMM can be guaranteed when the dual step…
This paper studies a class of convex Finite-sum Coupled Compositional Optimization (cFCCO) problems with applications including group distributionally robust optimization (GDRO) and learning with imbalanced data. To better address these…
Objective functions in large-scale machine-learning and artificial intelligence applications often live in high dimensions with strong non-convexity and massive local minima. First-order methods, such as the stochastic gradient method and…
Cognitive-Driven Development (CDD) is a coding design technique that aims to reduce the cognitive effort that developers place in understanding a given code unit (e.g., a class). By following CDD design practices, it is expected that the…
This paper describes a novel method to solve average-reward semi-Markov decision processes, by reducing them to a minimal sequence of cumulative reward problems. The usual solution methods for this type of problems update the gain (optimal…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
Adaptive systems must strike a balance between prediction and surprise to thrive in uncertain environments. We propose an information-theoretic balance function, $ f(p) = -(1 - p)\ln(1 - p) + \ln p $, which quantifies the net informational…
Proximal Policy Optimization (PPO) is widely regarded as one of the most successful deep reinforcement learning algorithms, known for its robustness and effectiveness across a range of problems. The PPO objective encourages the importance…
Many circumstances of practical importance have performance or success metrics which exist implicitly---in the eye of the beholder, so to speak. Tuning aspects of such problems requires working without defined metrics and only considering…
We study online learning in constrained Markov decision processes (CMDPs) in which rewards and constraints may be either stochastic or adversarial. In such settings, Stradi et al.(2024) proposed the first best-of-both-worlds algorithm able…
In the Bamboo Garden Trimming Problem (BGT), there is a garden populated by n bamboos b(1), b(2), ... , b(n)$ with daily growth rates h(1) >= h(2) >= ... >= h(n). We assume that the initial heights of bamboos are zero. A gardener is in…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an experienced expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work,…
Meta-heuristic algorithms are widely used to tackle complex optimization problems, including nonlinear, multimodal, and high-dimensional tasks. However, many existing methods suffer from premature convergence, limited exploration, and…
DPO is an effective preference optimization algorithm. However, the DPO-tuned models tend to overfit on the dispreferred samples, manifested as overly long generations lacking diversity. While recent regularization approaches have…
Figure drawing is often used as part of dementia screening protocols. The Survey of Health Aging and Retirement in Europe (SHARE) has adopted three drawing tests from Addenbrooke's Cognitive Examination III as part of its questionnaire…
In this paper, we develop new efficient projection-free algorithms for Online Convex Optimization (OCO). Online Gradient Descent (OGD) is an example of a classical OCO algorithm that guarantees the optimal $O(\sqrt{T})$ regret bound.…
Multiresolution topology optimization (MTO) methods involve decoupling of the design and analysis discretizations, such that a high-resolution design can be obtained at relatively low analysis costs. Recent studies have shown that the MTO…
The U.S. Food and Drug Administration (FDA) launched Project Optimus to shift the objective of dose selection from the maximum tolerated dose to the optimal biological dose (OBD), optimizing the benefit-risk tradeoff. One approach…