Inverse optimal control can be used to characterize behavior in sequential decisionmaking tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce a probabilistic approach to inverse optimal control for partially observable stochastic non-linear systems with unobserved action signals, which unifies previous approaches to inverse optimal control with maximum causal entropy formulations. Using an explicit model of the noise characteristics of the sensory and motor systems of the agent in conjunction with local linearization techniques, we derive an approximate likelihood function for the model parameters, which can be computed within a single forward pass.

Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased simulations seldom produce them. Transition Path Theory (TPT) provides a rigorous statistical framework for analyzing such events: it characterizes the ensemble of reactive trajectories between two designated metastable states (reactant and product), and its central object--the committor function, which gives the probability that the system will next reach the product rather than the reactant--encodes all essential kinetic and thermodynamic information. We introduce a framework that casts committor estimation as a stochastic optimal control (SOC) problem. In this formulation the committor defines a feedback control--proportional to the gradient of its logarithm--that actively steers trajectories toward the reactive region, thereby enabling efficient sampling of reactive paths. To solve the resulting hitting-time control problem we develop two complementary objectives: a direct backpropagation loss and a principled off-policy Value Matching loss, for which we establish first-order optimality guarantees. We further address metastability, which can trap controlled trajectories in intermediate basins, by introducing an alternative sampling process that preserves the reactive current while lowering effective energy barriers. On benchmark systems, the framework yields markedly more accurate committor estimates, reaction rates, and equilibrium constants than existing methods.

We demonstrate that these limitations can be sidestepped by reframing the generative process as a discrete optimal control episode.

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs.

Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable formulations. In this paper, we present a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. Specifically, we demonstrate how Doob's $h$-transform, the fundamental tool for constructing diffusion bridges, can be derived from the SOC perspective and expanded to infinite dimensions. This expansion presents a challenge, as infinite-dimensional spaces typically lack closed-form densities. Leveraging our theory, we establish that solving the optimal control problem with a specific objective function choice is equivalent to learning diffusion-based generative models. We propose two applications: 1) learning bridges between two infinite-dimensional distributions and 2) generative models for sampling from an infinite-dimensional distribution. Our approach proves effective for diverse problems involving continuous function space representations, such as resolution-free images, time-series data, and probability density functions.

This paper develops a unified perspective on several stochastic optimal control formulations through the lens of Kullback-Leibler regularization. We propose a central problem that separates the KL penalties on policies and transitions, assigning them independent weights, thereby generalizing the standard trajectory-level KL-regularization commonly used in probabilistic and KL-regularized control. This generalized formulation acts as a generative structure allowing to recover various control problems. These include the classical Stochastic Optimal Control (SOC), Risk-Sensitive Optimal Control (RSOC), and their policy-based KL-regularized counterparts. The latter we refer to as soft-policy SOC and RSOC, facilitating alternative problems with tractable solutions. Beyond serving as regularized variants, we show that these soft-policy formulations majorize the original SOC and RSOC problem. This means that the regularized solution can be iterated to retrieve the original solution. Furthermore, we identify a structurally synchronized case of the risk-seeking soft-policy RSOC formulation, wherein the policy and transition KL-regularization weights coincide. Remarkably, this specific setting gives rise to several powerful properties such as a linear Bellman equation, path integral solution, and, compositionality, thereby extending these computationally favourable properties to a broad class of control problems.

The home space for optimal control is a Sobolev space. The home space for pseudospectral theory is also a Sobolev space. It thus seems natural to combine pseudospectral theory with optimal control theory and construct ``pseudospectral optimal control theory,'' a term coined by Ross. In this paper, we review key theoretical results in pseudospectral optimal control that have proven to be critical for a successful flight. Implementation details of flight demonstrations onboard NASA spacecraft are discussed along with emerging trends and techniques in both theory and practice. The 2011 launch of pseudospectral optimal control in embedded platforms is changing the way in which we see solutions to challenging control problems in aerospace and autonomous systems.