相关论文: Language Generation as Optimal Control: Closed-Loo…
We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…
Stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than the the ones when the delay appears only in the state. This is particularly true when we look at the…
We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…
This paper investigates controllable generation for large language models (LLMs) with prompt-based control, focusing on Lexically Constrained Generation (LCG). We systematically evaluate the performance of LLMs on satisfying lexical…
This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on…
In this paper, a stochastic optimal control problem is investigated in which the system is governed by a stochastic functional differential equation. In the framework of functional It\^o calculus, we build the dynamic programming principle…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
Diffusion models have seen immense success in modelling continuous data across a range of domains such as vision and audio. Despite the challenges of adapting diffusion models to discrete data, recent work explores their application to text…
This paper studies stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, indicating its…
Despite the growing success of diffusion models in continuous-valued domains (e.g., images), similar efforts for discrete domains such as text have yet to match the performance of autoregressive language models. In this work, we present…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in…
Text generation aims to produce human-like natural language output for down-stream tasks. It covers a wide range of applications like machine translation, document summarization, dialogue generation and so on. Recently deep neural…
Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have…
Stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than the the ones when the delay appears only in the state. This is particularly true when we look at the…
We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow…
In this paper, we adapt stochastic Perron's method to analyze a stochastic target problem with unbounded controls in a jump diffusion set-up. With this method, we construct a viscosity sub-solution and super-solution to the associated…
This paper is concerned with the optimal control of hysteresis-reaction-diffusion systems. We study a control problem with two sorts of controls, namely distributed control functions, or controls which act on a part of the boundary of the…
Recent works have demonstrated success in controlling sentence attributes ($e.g.$, sentiment) and structure ($e.g.$, syntactic structure) based on the diffusion language model. A key component that drives theimpressive performance for…