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

Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…

We introduce a regulated stochastic diffusion model for the recycling rate and formulate a joint control problem over production and process innovation via the dynamics of recycling investment and product pricing. The resulting stochastic…

The autoregressive decoding for text generation in large language models (LLMs), while widely used, is inherently suboptimal due to the lack of a built-in mechanism to perform refinement and/or correction of the generated content. In this…

Language diffusion models aim to improve sampling speed and coherence over autoregressive LLMs. We introduce Neural Flow Diffusion Models for language generation, an extension of NFDM that enables the straightforward application of…

The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…

Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is…

This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…

Previous work on controllable text generation has explored the idea of control from the latent space, such as optimizing a representation with attribute-related classifiers or sampling a representation from relevant discrete samples.…

This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and…

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion…

We investigate the learning task of language generation in the limit, but shift focus from the traditional time-of-last-mistake metric of a generator's success to a new notion of "mistake-bounded generation." While existing results for…

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…

Citation generation aims to generate a citation sentence that refers to a chosen paper in the context of a manuscript. However, a rigid citation generation process is at odds with an author's desire to control specific attributes, such as…

Controllable diffusion generation often relies on various heuristics that are seemingly disconnected without a unified understanding. We bridge this gap with Diffusion Controller (DiffCon), a unified control-theoretic view that casts…

In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…

We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…

Diffusion Language models (DLMs) are a promising avenue for text generation due to their practical properties on tractable controllable generation. They also have the advantage of not having to predict text autoregressively. However,…

This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…

The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic processes have increasingly been applied to sample generation.…

This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…