Related papers: Operator Splitting Value Iteration
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or…
Existing Flow Matching (FM) text-to-image models suffer from two critical bottlenecks under multi-task alignment: the reward sparsity induced by scalar-valued rewards, and the gradient interference arising from jointly optimizing…
We consider monotone inclusion problems where the operators may be expectation-valued, a class of problems that subsumes convex stochastic optimization problems as well as subclasses of stochastic variational inequality and equilibrium…
A promising way to improve the sample efficiency of reinforcement learning is model-based methods, in which many explorations and evaluations can happen in the learned models to save real-world samples. However, when the learned model has a…
In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems. Similar to the gradient (operator) projection method, OE updates one single search sequence by solving…
Despite significant progress, Vision-Language Models (VLMs) still struggle with complex visual reasoning, where multi-step dependencies cause early errors to cascade through the reasoning chain. Existing post-training paradigms are limited:…
Value iteration is a fundamental algorithm for solving Markov Decision Processes (MDPs). It computes the maximal $n$-step payoff by iterating $n$ times a recurrence equation which is naturally associated to the MDP. At the same time, value…
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…
Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the…
We study episodic reinforcement learning in non-stationary linear (a.k.a. low-rank) Markov Decision Processes (MDPs), i.e, both the reward and transition kernel are linear with respect to a given feature map and are allowed to evolve either…
This paper focuses on the design of an asynchronous dual solver suitable for embedded model predictive control (MPC) applications. The proposed solver relies on a state-of-the-art variance reduction (VR) scheme, previously used in the…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Large language models (LLMs) often struggle with maintaining accuracy throughout multiple multiple reasoning steps, especially in mathematical reasoning where an error in earlier steps can propagate to subsequent ones and it ultimately…
Over the past few years, the federated learning ($\texttt{FL}$) community has witnessed a proliferation of new $\texttt{FL}$ algorithms. However, our understating of the theory of $\texttt{FL}$ is still fragmented, and a thorough, formal…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require…
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…
Modern reasoning agents are increasingly evaluated on their ability to generate multiple valid solution paths, plans, or tool-use traces for a given input. Standard reward-maximizing RL tends to collapse onto the most easily reinforced…
Dynamic Optimization Problems (DOPs) are challenging to address due to their complex nature, i.e., dynamic environment variation. Evolutionary Computation methods are generally advantaged in solving DOPs since they resemble dynamic…
In many finite horizon episodic reinforcement learning (RL) settings, it is desirable to optimize for the undiscounted return - in settings like Atari, for instance, the goal is to collect the most points while staying alive in the long…