Nonparametric Approximate Dynamic Programming via the Kernel Method

Non-parametric Approximate Dynamic Programming via the Kernel Method

This paper presents a novel non-parametric approximate dynamic programming (ADP) algorithm that enjoys graceful approximation and sample complexity guarantees. In particular, we establish both theoretically and computationally that our proposal can serve as a viable alternative to state-of-the-art parametric ADP algorithms, freeing the designer from carefully specifying an approximation archite...

Approximate Dynamic Programming via Linear Programming

The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of preselected basis functions to the dynamic programming costtogo function. We develop...

Approximate Dynamic Programming via Iterated Bellman Inequalities

In this paper we introduce new methods for finding functions that lower bound the value function of a stochastic control problem, using an iterated form of the Bellman inequality. Our method is based on solving linear or semidefinite programs, and produces both a bound on the optimal objective, as well as a suboptimal policy that appears to works very well. These results extend and improve boun...

Transaction-Cost-Conscious Pairs Trading via Approximate Dynamic Programming

In this paper, we develop an algorithm that optimizes logarithmic utility in pairs trading. We assume price processes for two assets, with transaction cost linear with respect to the rate of change in portfolio weights. We then solve the optimization problem via a linear programming approach to approximate dynamic programming. Our simulation results show that when asset price volatility and tra...

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