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This note lays part of the theoretical ground for a definition of differential systems modeling reinforcement learning in continuous time non-Markovian rough environments. Specifically we focus on optimal relaxed control of rough equations…
This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform…
We investigate an entropy-regularized reinforcement learning (RL) approach to optimal stopping problems motivated by real option models. Classical stopping rules are strict and non-randomized, limiting natural exploration in RL settings. To…
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…
Reinforcement Learning (RL) has achieved remarkable success in safety-critical areas, but it can be weakened by adversarial attacks. Recent studies have introduced "smoothed policies" in order to enhance its robustness. Yet, it is still…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
The Lipschitz bandit problem extends stochastic bandits to a continuous action set defined over a metric space, where the expected reward function satisfies a Lipschitz condition. In this work, we introduce a new problem of Lipschitz bandit…
We obviate the use of observers for the purpose of output feedback tracking control of Lagrangian systems and solve some long-standing yet well-documented open problems. As often implemented in control practice, we replace unavailable…
This paper studies the continuous-time reinforcement learning for stochastic singular control with the application to an infinite-horizon irreversible reinsurance problems. The singular control is equivalently characterized as a pair of…
Despite the many recent advances in reinforcement learning (RL), the question of learning policies that robustly satisfy state constraints under unknown disturbances remains open. In this paper, we offer a new perspective on achieving…
In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of…
We study the stochastic Landau-Lifshitz-Bloch equation perturbed by pure jump noise. In order to understand and also control the fluctuations and jumps observed in the hysteresis loop, we add noise and an external control to the effective…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
The naive application of Reinforcement Learning algorithms to continuous control problems -- such as locomotion and manipulation -- often results in policies which rely on high-amplitude, high-frequency control signals, known colloquially…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and…
We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a…
We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show…
This paper addresses the following question: "Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuous-time system. If we choose the parameters of an event/self-triggering mechanism appropriately, is the…
Classical stability theory for stochastic programming relies on the Wasserstein-Fortet-Mourier duality, which requires the ground cost to be a distance. When using problem-dependent costs instead of metrics, this duality no longer yields…