# Loss Bounds for Approximate Influence-Based Abstraction

arXiv: https://arxiv.org/abs/2011.01788 · HTML: https://mlsanity.com/paper/2011.01788/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Factored Policy Gradients: Leveraging Structure for Efficient Learning in MOMDPs](https://mlsanity.com/paper/2102.10362/) (2021)
- [Influence-Augmented Local Simulators: A Scalable Solution for Fast Deep RL in Large Networked Systems](https://mlsanity.com/paper/2202.01534/) (2022)
- [Online Planning in POMDPs with Self-Improving Simulators](https://mlsanity.com/paper/2201.11404/) (2022)
- [Distributed Influence-Augmented Local Simulators for Parallel MARL in Large Networked Systems](https://mlsanity.com/paper/2207.00288/) (2022)

## Abstract (arXiv)

Sequential decision making techniques hold great promise to improve the performance of many real-world systems, but computational complexity hampers their principled application. Influence-based abstraction aims to gain leverage by modeling local subproblems together with the 'influence' that the rest of the system exerts on them. While computing exact representations of such influence might be intractable, learning approximate representations offers a promising approach to enable scalable solutions. This paper investigates the performance of such approaches from a theoretical perspective. The primary contribution is the derivation of sufficient conditions on approximate influence representations that can guarantee solutions with small value loss. In particular we show that neural networks trained with cross entropy are well suited to learn approximate influence representations. Moreover, we provide a sample based formulation of the bounds, which reduces the gap to applications. Finally, driven by our theoretical insights, we propose approximation error estimators, which empirically reveal to correlate well with the value loss.