Related papers: Entropy-Regularized Certainty-Equivalent Bellman P…
The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting…
This paper addresses the design of linear and nonlinear stabilization procedures for high-order continuous Galerkin (CG) finite element discretizations of scalar conservation laws. We prove that the standard CG method is entropy…
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion 'factor' process. The…
In ergodic stochastic problems the limit of the value function $V_\lambda$ of the associated discounted cost functional with infinite time horizon is studied, when the discounted factor $\lambda$ tends to zero. These problems have been well…
This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log…
This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a…
Reliable long-horizon value prediction is difficult in offline reinforcement learning because fitted value methods combine bootstrapping, function approximation, and distribution shift, while standard guarantees often require Bellman…
Optimized certainty equivalents (OCEs) is a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability and the fact that it encompasses important examples, including entropic risk…
We study entropy-regularized mean-variance portfolio optimization under Bayesian drift uncertainty. Gaussian policies remain optimal under partial information, the value function is quadratic in wealth, and belief-dependent coefficients…
In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect…
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…
Exploration is a crucial and distinctive aspect of reinforcement learning (RL) that remains a fundamental open problem. Several methods have been proposed to tackle this challenge. Commonly used methods inject random noise directly into the…
This paper studies value iteration for infinite horizon contracting Markov decision processes under convexity assumptions and when the state space is uncountable. The original value iteration is replaced with a more tractable form and the…
We consider infinite-horizon $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies $\pi_1,...,\pi_k$ it…
In this paper, we present a generalization of the certainty equivalence principle of stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as…
A pricing principle is introduced for non-attainable $q$-exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent claim under the ``distorted Radon-Nikodym derivative'' and…
Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…
We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The method is closely related to the classic Relative Entropy Policy Search (REPS) algorithm of Peters…
We consider an entropy-regularized version of optimal density control of deterministic discrete-time linear systems. Entropy regularization, or a maximum entropy (MaxEnt) method for optimal control has attracted much attention especially in…
We study the exploration problem with approximate linear action-value functions in episodic reinforcement learning under the notion of low inherent Bellman error, a condition normally employed to show convergence of approximate value…