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

We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…

The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…

In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…

In this paper, we consider a company can simultaneously reduce its emissions and buy carbon allowances at any time. We establish an optimal control model involving two stochastic processes with two control variables, which is a singular…

In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…

Probabilistic language generators are theoretically modeled as discrete stochastic processes, yet standard decoding strategies (Top-k, Top-p) impose static truncation rules that fail to accommodate the dynamic information density of natural…

We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate its effectiveness using examples from multi-agent path finding. Our approach yields controls in a feedback…

Sampling from probability densities is a common challenge in fields such as Uncertainty Quantification (UQ) and Generative Modelling (GM). In GM in particular, the use of reverse-time diffusion processes depending on the log-densities of…

In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…

We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control…

Current language models demonstrate remarkable proficiency in text generation. However, for many applications it is desirable to control attributes, such as sentiment, or toxicity, of the generated language -- ideally tailored towards each…

We provide a data-driven framework for optimal control of a continuous-time stochastic dynamical system. The proposed framework relies on the linear operator theory involving linear Perron-Frobenius (P-F) and Koopman operators. Our first…

This work introduces MotionLCM, extending controllable motion generation to a real-time level. Existing methods for spatial-temporal control in text-conditioned motion generation suffer from significant runtime inefficiency. To address this…

Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline…

In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the agents shall be minimized, while the…

Semantic control entails steering LM generations towards satisfying subtle non-lexical constraints, e.g., toxicity, sentiment, or politeness, attributes that can be captured by a sequence-level verifier. It can thus be viewed as sampling…

This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…

Controlled text generation allows for enforcing user-defined constraints on large language model outputs, an increasingly important field as LLMs become more prevalent in everyday life. One common approach uses energy-based decoding, which…

We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoidance. These problems immediately become high-dimensional,…

A theoretical optimization method of high-harmonic-generation (HHG) is developed in the framework of optimal-control-theory (OCT). The target of optimization is the emission radiation of a particular frequency. The OCT formulation includes…