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Reinforcement learning has become an essential algorithm for generating complex robotic behaviors. However, to learn such behaviors, it is necessary to design a reward function that describes the task, which often consists of multiple…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

Retrieval-augmented generation combined with reinforcement learning has shown promise for grounding large language models in trustworthy medical evidence. However, existing methods rely on exact-match binary rewards, which in clinical…

Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then…

Large language model (LLM) alignment algorithms typically consist of post-training over preference pairs. While such algorithms are widely used to enable safety guardrails and align LLMs with general human preferences, we show that…

This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

Retrieval-Augmented Generation (RAG) has demonstrated significant effectiveness in enhancing large language models (LLMs) for complex multi-hop question answering (QA). For multi-hop QA tasks, current iterative approaches predominantly rely…

Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…

Autoregressive decoding in Large Language Models (LLMs) generates one token per step, causing high inference latency. Speculative decoding (SD) mitigates this through a guess-and-verify strategy, but existing training-free variants face…

Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with…

A new predictor-corrector type incremental algorithm is proposed for the exact construction of weighted straight skeletons of 2D general planar polygons of arbitrary complexity based on the notion of deforming polygon. In the proposed…

This paper proposes a differentiable robust LQR layer for reinforcement learning and imitation learning under model uncertainty and stochastic dynamics. The robust LQR layer can exploit the advantages of robust optimal control and…

This paper investigates the stochastic optimization problem with a focus on developing scalable parallel algorithms for deep learning tasks. Our solution involves a reformation of the objective function for stochastic optimization in neural…

We propose a new two stage algorithm LING for large scale regression problems. LING has the same risk as the well known Ridge Regression under the fixed design setting and can be computed much faster. Our experiments have shown that LING…

A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online…

This paper introduces an approach for training o1-like RAG models that retrieve and reason over relevant information step by step before generating the final answer. Conventional RAG methods usually perform a single retrieval step before…

We consider a problem of linear model selection in the presence of both continuous and categorical predictors. Feasible models consist of subsets of numerical variables and partitions of levels of factors. A new algorithm called delete or…

In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…

Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased…