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Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…
The rising successes of RL are propelled by combining smart algorithmic strategies and deep architectures to optimize the distribution of returns and visitations over the state-action space. A quantitative framework to compare the learning…
The rapid emergence of diverse large language models (LLMs) has spurred the development of LLM routers that assign user queries to the most suitable model. However, existing LLM routers typically perform a single-round, one-to-one mapping…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We propose a novel approach for sampling-based and control-based motion planning that combines a representation of the environment obtained via a modified version of optimal Rapidly-exploring Random Trees (RRT*), with landmark-based…
We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic…
A key challenge in machine learning is to design interpretable models that can reduce their inputs to the best subset for making transparent predictions, especially in the clinical domain. In this work, we propose a certifiably optimal…
As one of the most fundamental concepts in transportation science, Wardrop equilibrium (WE) has always had a relatively weak behavioral underpinning. To strengthen this foundation, one must reckon with bounded rationality in human…
In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted sum of two conflicting objectives, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of the…
We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk,…
Probit models are useful for modeling correlated discrete responses in many disciplines, including consumer choice data in economics and marketing. However, the Gaussian latent variable feature of probit models coupled with identification…
Checkpoint selection for multimodal large language models (MLLMs) presents significant challenges when performance differentials are marginal and evaluation signals are prone to noise. Existing methodologies rely heavily on static…
Large Language Models (LLMs) have demonstrated impressive ability in generation and reasoning tasks but struggle with handling up-to-date knowledge, leading to inaccuracies or hallucinations. Retrieval-Augmented Generation (RAG) mitigates…
We propose a control framework that integrates model-based bipedal locomotion with residual reinforcement learning (RL) to achieve robust and adaptive walking in the presence of real-world uncertainties. Our approach leverages a model-based…
Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…
We consider a dynamic pricing problem in network revenue management where customer behavior is predicted by a choice model, i.e., the multinomial logit (MNL) model. The problem, even in the static setting (i.e., customer demand remains…
This work develops an LLM-based optimization framework ensuring strict constraint satisfaction in network optimization. While LLMs possess contextual reasoning capabilities, existing approaches often fail to enforce constraints, causing…
With the widespread deployment of large language models (LLMs) such as GPT4, BART, and LLaMA, the need for a system that can intelligently select the most suitable model for specific tasks while balancing cost, latency, accuracy, and…