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In this paper, we present a novel algorithm named synchronous integral Q-learning, which is based on synchronous policy iteration, to solve the continuous-time infinite horizon optimal control problems of input-affine system dynamics. The…
Neural network approaches that parameterize value functions have succeeded in approximating high-dimensional optimal feedback controllers when the Hamiltonian admits explicit formulas. However, many practical problems, such as the space…
Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the…
In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Levy type noises with distributed control process acting on the state equation. We use the dynamic programming approach for the second order…
In reinforcement learning (RL), the long-term behavior of decision-making policies is evaluated based on their average returns. Distributional RL has emerged, presenting techniques for learning return distributions, which provide additional…
This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a…
The ability to quickly learn new knowledge (e.g. new classes or data distributions) is a big step towards human-level intelligence. In this paper, we consider scenarios that require learning new classes or data distributions quickly and…
Binary Neural Network (BNN) converts full-precision weights and activations into their extreme 1-bit counterparts, making it particularly suitable for deployment on lightweight mobile devices. While binary neural networks are typically…
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…
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…
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…
We present exponential error estimates and demonstrate an algebraic convergence rate for the homogenization of level-set convex Hamilton-Jacobi equations in i.i.d. random environments, the first quantitative homogenization results for these…
Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the…
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…
We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processes by establishing a new theoretical connection between…
We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…
The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton--Jacobi--Bellman (HJB) equation to be called…
In mathematical finance, many derivatives from markets with frictions can be formulated as optimal control problems in the HJB framework. Analytical optimal control can result in highly nonlinear PDEs, which might yield unstable numerical…