Related papers: Proving Almost-Sure Termination of Probabilistic P…

We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…

In large language models (LLM)-based recommendation systems (LLM-RSs), accurately predicting user preferences by leveraging the general knowledge of LLMs is possible without requiring extensive training data. By converting recommendation…

Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs…

We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work,…

We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…

In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…

Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can…

Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems (TRSs) automatically. We adapt the dependency pair framework to the probabilistic setting in order to prove almost-sure innermost…

We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…

We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have…

Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…

Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…

Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a…

Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…