# From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming

arXiv: https://arxiv.org/abs/1701.06379 · HTML: https://mlsanity.com/paper/1701.06379/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2017.

## Built on by (most cited first, 5 of 5)

- [Proximal Point Imitation Learning](https://mlsanity.com/paper/2209.10968/) (2022)
- [Efficient Performance Bounds for Primal-Dual Reinforcement Learning from Demonstrations](https://mlsanity.com/paper/2112.14004/) (2021)
- [From Optimization to Control: Quasi Policy Iteration](https://mlsanity.com/paper/2311.11166/) (2023)
- [Randomized algorithms and PAC bounds for inverse reinforcement learning in continuous spaces](https://mlsanity.com/paper/2405.15509/) (2024)
- [Control and Reinforcement Learning through the Lens of Optimization: An Algorithmic Perspective](https://mlsanity.com/paper/2512.07377/) (2025)

## Abstract (arXiv)

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the recent developments in two areas of randomized optimization and first order methods, leading to a priori as well as a posterior performance guarantees. We illustrate the generality and implications of our theoretical results in the special case of the long-run average cost and discounted cost optimal control problems for Markov decision processes on Borel spaces. The applicability of the theoretical results is demonstrated through a constrained linear quadratic optimal control problem and a fisheries management problem.