Policy Gradients with Variance Related Risk Criteria (1206.6404v1)

Abstract: Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the standard deviation adjusted reward. It is known that optimizing many of the variance related risk criteria is NP-hard. In this paper we devise a framework for local policy gradient style algorithms for reinforcement learning for variance related criteria. Our starting point is a new formula for the variance of the cost-to-go in episodic tasks. Using this formula we develop policy gradient algorithms for criteria that involve both the expected cost and the variance of the cost. We prove the convergence of these algorithms to local minima and demonstrate their applicability in a portfolio planning problem.

• The paper introduces policy gradient algorithms that balance expected returns with trajectory variance, enabling risk-sensitive learning.
• It derives precise gradient expressions using reformulations for both model-based and simulation-based approaches to manage computation efficiently.
• Empirical results in portfolio management show that risk-sensitive strategies yield more statistically stable outcomes than traditional reward maximization.

Policy Gradients with Variance Related Risk Criteria

The paper "Policy Gradients with Variance Related Risk Criteria" by Aviv Tamar et al. presents a sophisticated approach to risk management in reinforcement learning (RL) through the lens of variance-related risk criteria. Traditional RL techniques primarily focus on maximizing cumulative rewards, often neglecting the risk associated with decision sequences. This research shifts the focus to variance-based risk criteria, aiming to address both expected costs and the variability of returns, a concern pertinent in domains like finance and process control.

The authors start by highlighting the NP-hardness of optimizing variance-related criteria in dynamic decision-making. It introduces a new formula to calculate the variance of the cost-to-go in episodic tasks within RL environments, a critical step that enables the formulation of policy gradient algorithms sensitive to risk measures. Unlike classical utility-based risk measures, which, like exponential utility functions, require parameter selection fraught with subjectivity, variance is posited as an intuitive and practical alternative.

Key contributions of the paper include:

1. Policy Gradient Algorithms: The authors develop a framework allowing both model-based and model-free policy gradient algorithms, optimized for trajectory variance and expected cost performance criteria. Notably, these algorithms converge to local minima and are applicable to performance constraints that include variance considerations.
2. Algorithmic Feasibility: Through a series of reformulations and assumptions, the authors derive precise gradient expressions to control trajectory variance. The method presented sidesteps the challenges posed by non-convexity and significant computational expense typically associated with variance optimization problems.
3. Simulation-based approach: Acknowledging scenarios where the model parameters might be unknown, an estimation method based on simulation is proposed. This method leverages the likelihood ratio method to efficiently compute unbiased gradient estimates of performance measures, enhancing algorithm applicability to diverse RL environments.
4. Empirical Validation: Using a portfolio management scenario characterized by both liquid and non-liquid assets, the paper demonstrates the numerical applicability of the algorithms. It shows that by employing different criteria such as maximizing rewards, controlling variance, and maximizing the Sharpe Ratio, varying levels of risk and reward trade-offs can be captured. Notably, risk-sensitive strategies yielded less aggressive and more statistically stable outcomes compared to reward-maximizing strategies, which entail higher variability.

The proposed algorithms have significant implications in areas where risk is as important as reward, such as finance, autonomous systems, and machine learning applied in uncertain environments. By effectively integrating risk measures like variance into RL, the approach could lead to more robust decision-making frameworks that better reflect real-world concerns.

In future work, the exploration of percentile criteria and the use of variance in accelerating convergence in policy optimization underscores the potential for further advancements. Additionally, integration with other RL paradigms and enhancement of risk measures could broaden the technique's applicability, particularly in high-stakes environments where risk aversion is paramount.

In conclusion, this research venture opens a conduit for tailored RL methodologies that incorporate variance as a legitimate risk measure, paving the way for more informed decision-making frameworks that resonate across a spectrum of risk-sensitive applications.