Related papers: Output-Sensitive Adaptive Metropolis-Hastings for …

Aligning general-purpose large language models (LLMs) to downstream tasks often incurs significant training adjustment costs. Prior research has explored various avenues to enhance alignment efficiency, primarily through minimal-data…

Alternating Direction Method of Multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting agents locally estimate the optimal solution of an…

We analyse computational efficiency of Metropolis-Hastings algorithms with AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g. HMC). By…

In this study, we investigate the performance of the Metropolis-adjusted Langevin algorithm in a setting with constraints on the support of the target distribution. We provide a rigorous analysis of the resulting Markov chain, establishing…

Experimental calibration of dynamic thermal models is required for model predictive control and characterization of building energy performance. In these applications, the uncertainty assessment of the parameter estimates is decisive; this…

We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in parallel. To this end, we partition the data and distribute the resulting subproblems among the available…

Large Language Models (LLMs), with billions of parameters, present significant challenges for full finetuning due to the high computational demands, memory requirements, and impracticality of many real-world applications. When faced with…

Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…

There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian…

Locality-sensitive hashing (LSH) is an effective randomized technique widely used in many machine learning tasks. The cost of hashing is proportional to data dimensions, and thus often the performance bottleneck when dimensionality is high…

Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…

Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…

A well-known difficult problem regarding Metropolis-Hastings algorithms is to get sharp bounds on their convergence rates. Moreover, a fundamental but often overlooked problem in Markov chain theory is to study the convergence rates for…

A popular approach for improving the correctness of output from large language models (LLMs) is Self-Consistency - poll the LLM multiple times and output the most frequent solution. Existing Self-Consistency techniques always generate a…

This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…

With the rapid development of natural language processing technology, large-scale language models (LLM) have achieved remarkable results in a variety of tasks. However, how to effectively train these huge models and improve their…

Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in nonlinear state space models by combining Markov chain Monte Carlo (MCMC) and particle filtering. The latter is used to estimate the intractable likelihood. In…

Recent advances in test-time alignment methods, such as Best-of-N sampling, offer a simple and effective way to steer language models (LMs) toward preferred behaviors using reward models (RM). However, these approaches can be…

Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…

We introduce Adversarial Policy Optimization (AdvPO), a novel solution to the pervasive issue of reward over-optimization in Reinforcement Learning from Human Feedback (RLHF) for Large Language Models (LLMs). Over-optimization occurs when a…