Summary of Lagrangian Index Policy For Restless Bandits with Average Reward, by Konstantin Avrachenkov et al.
Lagrangian Index Policy for Restless Bandits with Average Reward
by Konstantin Avrachenkov, Vivek S. Borkar, Pratik Shah
First submitted to arxiv on: 17 Dec 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Optimization and Control (math.OC); Probability (math.PR)
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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 This research paper investigates the Lagrangian Index Policy (LIP) for restless multi-armed bandits with long-run average reward. The authors compare LIP’s performance to that of the Whittle Index Policy (WIP), which is known to be asymptotically optimal under certain conditions. While their performances are similar in most cases, LIP outperforms WIP when WIP shows poor results. To obtain online learning schemes for LIP in a model-free setting, the authors propose reinforcement learning algorithms based on tabular and neural network (NN) approaches. These algorithms require significantly less memory than analogous schemes for WIP. The paper also provides analytical calculations of the Lagrangian index for the restart model, which is relevant to web crawling and minimizing the weighted age of information. Additionally, the authors present a new proof of asymptotic optimality in the case of homogeneous bandits as the number of arms approaches infinity, relying on exchangeability and de Finetti’s theorem. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores how to make good decisions when faced with many options that change over time. The researchers compare two different strategies: Lagrangian Index Policy (LIP) and Whittle Index Policy (WIP). LIP is better than WIP in some cases, especially when things don’t go well for WIP. To help computers learn to make good decisions using LIP, the authors suggest new ways of using reinforcement learning. These methods require less memory than similar approaches for WIP. The paper also shows how to calculate a special value called the Lagrangian index, which is important for tasks like searching the internet and keeping track of information. |
Keywords
» Artificial intelligence » Neural network » Online learning » Reinforcement learning
