Related papers: On Feedback Control in Kelly Betting: An Approxima…
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
Approximate computing trades off accuracy of results for resources such as energy or computing time. There is a large and rapidly growing literature on approximate computing that has focused mostly on showing the benefits of approximation.…
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…
We develop horizon-aware anytime-valid tests and confidence sequences for bounded means under a strict deadline $N$. Using the betting/e-process framework, we cast horizon-aware betting as a finite-horizon optimal control problem with state…
In this paper, a leader-follower stochastic differential game is studied for a linear stochastic differential equation with a quadratic cost functional. The coefficients in the state equation and the weighting matrices in the cost…
A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
In this work, we consider the problem of minimising the social cost in atomic congestion games. For this problem, we provide tight computational lower bounds along with taxation mechanisms yielding polynomial time algorithms with optimal…
Approximating a Nash equilibrium is currently the best performing approach for creating poker-playing programs. While for the simplest variants of the game, it is possible to evaluate the quality of the approximation by computing the value…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the…
Stochastic Model Predictive Control addresses uncertainties by incorporating chance constraints that provide probabilistic guarantees of constraint satisfaction. However, simultaneously optimizing over the risk allocation and the feedback…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In…
Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…
This paper presents a novel approach for optimizing betting strategies in sports gambling by integrating Von Neumann-Morgenstern Expected Utility Theory, deep learning techniques, and advanced formulations of the Kelly Criterion. By…
This study presents a rigorous mathematical approach to the optimization of round and betting policies in Blackjack, using Markov Decision Processes (MDP) and Expected Utility Theory. The analysis considers a direct confrontation between a…
The entropy regularization is inspired by information entropy from machine learning and the ideas of exploration and exploitation in reinforcement learning, which appears in the control problem to design an approximating algorithm for the…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…