相关论文: Language Generation as Optimal Control: Closed-Loo…

This paper mainly establishes the finite-horizon stochastic bounded real lemma, and then solves the $H_{\infty}$ control problem for discrete-time stochastic linear systems defined on the separable Hilbert spaces, thereby unifying the…

Despite the remarkable advances in language modeling, current mainstream decoding methods still struggle to generate texts that align with human texts across different aspects. In particular, sampling-based methods produce less-repetitive…

In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…

Diffusion models emerged as a leading approach in text-to-image generation, producing high-quality images from textual descriptions. However, attempting to achieve detailed control to get a desired image solely through text remains a…

Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on…

This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…

Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules,…

We address the crucial yet underexplored stability properties of the Hamilton--Jacobi--Bellman (HJB) equation in model-free reinforcement learning contexts, specifically for Lipschitz continuous optimal control problems. We bridge the gap…

Autoregressive models for text sometimes generate repetitive and low-quality output because errors accumulate during the steps of generation. This issue is often attributed to exposure bias - the difference between how a model is trained,…

Generating human motion that satisfies customized zero-shot goal functions, enabling applications such as controllable character animation and behavior synthesis for virtual agents, is a critical capability. While current approaches handle…

This paper investigates the distributed optimal output consensus problem of heterogeneous linear multi-agent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to…

This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…

While large language models (LLMs) have made significant strides in generating coherent and contextually relevant text, they often function as opaque black boxes, trained on vast unlabeled datasets with statistical objectives, lacking an…

The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…

This paper provides an in-depth examination of the concept of semantic diffusion as a complementary instrument to large language models (LLMs) for design applications. Conventional LLMs and diffusion models fail to induce a convergent,…

In this manuscript we consider optimal control problems of stochastic differential equations with delays in the state and in the control. First, we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then,…

Optimal control and the associated second-order path-dependent Hamilton-Jacobi-Bellman (PHJB) equation are studied for unbounded functional stochastic evolution systems in Hilbert spaces. The notion of viscosity solution without…

Large Language Models (LLMs) excel at generating fluent text but struggle to enforce external constraints because they generate tokens sequentially without explicit control mechanisms. GenCP addresses this limitation by combining LLM…

Controlling the evolution of a many-body stochastic system from a disordered reference state to a structured target ensemble, characterized empirically through samples, arises naturally in non-equilibrium statistical mechanics and…

We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables…