Summary of Concentration Of Cumulative Reward in Markov Decision Processes, by Borna Sayedana et al.
Concentration of Cumulative Reward in Markov Decision Processes
by Borna Sayedana, Peter E. Caines, Aditya Mahajan
First submitted to arxiv on: 27 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Systems and Control (eess.SY); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A unified approach to characterize reward concentration in Markov Decision Processes (MDPs) is proposed, covering infinite-horizon settings, finite-horizon settings, law of large numbers, central limit theorem, law of iterated logarithms, Azuma-Hoeffding-type inequalities, and non-asymptotic version of the law of iterated logarithms. The approach relies on a novel martingale decomposition, policy evaluation fixed-point equation, and concentration results for martingale difference sequences. This framework has implications for sample path behavior of reward differences between stationary policies and rate-equivalence of alternative regret definitions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A group of researchers studied how rewards work in a special kind of math problem called Markov Decision Processes (MDPs). They found a way to understand how rewards behave over time, both in the long run and when looking at short periods. This helps us learn about the differences between different strategies for solving these problems. The new method uses some advanced math tricks to figure out how rewards work and has important implications for understanding what happens when we compare different ways of solving MDPs. |
