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Policy optimization (PO) is a key ingredient for reinforcement learning (RL). For control design, certain constraints are usually enforced on the policies to optimize, accounting for either the stability, robustness, or safety concerns on…
This article presents proposals for the design of reduced-order controllers for high-dimensional dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational…
Online convex optimization (OCO) is a powerful tool for learning sequential data, making it ideal for high precision control applications where the disturbances are arbitrary and unknown in advance. However, the ability of OCO-based…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
The Team Orienteering Problem (TOP) generalizes many real-world multi-robot scheduling and routing tasks that occur in autonomous mobility, aerial logistics, and surveillance applications. While many flavors of the TOP exist for planning in…
We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
We are interested in optimally driving a dynamical system that can be influenced by exogenous noises. This is generally called a Stochastic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle is the natural way of…
We explore deep Reinforcement Learning(RL) algorithms for scalping trading and knew that there is no appropriate trading gym and agent examples. Thus we propose gym and agent like Open AI gym in finance. Not only that, we introduce new RL…
Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm…
Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturally, such as port-Hamiltonian systems, optimal control, and…
While large language models (LLMs) have recently made tremendous progress towards solving challenging AI problems, they have done so at increasingly steep computational and API costs. We propose a novel strategy where we combine multiple…
We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By…
In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
When sales of a product are affected by randomness in demand, retailers can use dynamic pricing strategies to maximise their profits. In this article the pricing problem is formulated as a stochastic optimal control problem, where the…
A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and Integral of Squared Controller Output (ISCO) minimization based time domain optimal tuning of fractional-order (FO) PID or PI{\lambda}D{\mu} controller is…
This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spectral decomposition of the Koopman operator. The reduced…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…