Summary of Continuous-time Risk-sensitive Reinforcement Learning Via Quadratic Variation Penalty, by Yanwei Jia
Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty
by Yanwei Jia
First submitted to arxiv on: 19 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Systems and Control (eess.SY); Computational Finance (q-fin.CP); Portfolio Management (q-fin.PM)
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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 The paper investigates continuous-time risk-sensitive reinforcement learning (RL) under an entropy-regularized, exploratory diffusion process framework with exponential-form objectives. The risk-sensitive objective stems from either the agent’s risk attitude or a distributionally robust approach against model uncertainty. By drawing on Jia and Zhou’s martingale perspective (2023), the paper shows that the risk-sensitive RL problem is equivalent to ensuring the martingale property of a process involving value and q-functions, augmented with an additional penalty term: the quadratic variation of the value process. This characterization enables the straightforward adaptation of existing non-risk-sensitive RL algorithms by incorporating the realized variance of the value process. However, the conventional policy gradient representation is insufficient for risk-sensitive problems due to nonlinearities; q-learning offers a solution and extends to infinite horizon settings. The paper proves the convergence of its proposed algorithm for Merton’s investment problem and examines the impact of temperature parameters on learning behavior. Simulation experiments demonstrate how risk-sensitive RL improves finite-sample performance in linear-quadratic control. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how agents can make decisions that balance risk and reward while learning over time. It develops a new way to think about this problem, which is useful because traditional methods don’t work well when there’s uncertainty involved. The authors show that their approach can be used with existing algorithms, but it requires some adjustments. They also test their method on two specific problems and find that it improves performance in certain situations. |
Keywords
* Artificial intelligence * Diffusion * Reinforcement learning * Temperature
