Simplification of Risk Averse POMDPs with Performance Guarantees

This paper presents a framework for simplifying the evaluation of Conditional Value at Risk (CVaR) in Partially Observable Markov Decision Processes (POMDPs) by using computationally cheaper belief-MDP transition models, while providing theoretical performance guarantees for the resulting value function bounds.

Abstract

Risk averse decision making under uncertainty in partially observable domains is a fundamental problem in AI and essential for reliable autonomous agents. In our case, the problem is modeled using partially observable Markov decision processes (POMDPs), when the value function is the conditional value at risk (CVaR) of the return. Calculating an optimal solution for POMDPs is computationally intractable in general. In this work we develop a simplification framework to speedup the evaluation of the value function, while providing performance guarantees. We consider as simplification a computationally cheaper belief-MDP transition model, that can correspond, e.g., to cheaper observation or transition models. Our contributions include general bounds for CVaR that allow bounding the CVaR of a random variable X, using a random variable Y, by assuming bounds between their cumulative distributions. We then derive bounds for the CVaR value function in a POMDP setting, and show how to bound the value function using the computationally cheaper belief-MDP transition model and without accessing the computationally expensive model in real-time. Then, we provide theoretical performance guarantees for the estimated bounds. Our results apply for a general simplification of a belief-MDP transition model and support simplification of both the observation and state transition models simultaneously.

Method

The methodology of this paper involves developing a simplification framework to address the computational challenges of evaluating the Conditional Value at Risk (CVaR) in Partially Observable Markov Decision Processes (POMDPs). The authors propose using a computationally cheaper belief-MDP transition model as a simplification of the original model. They establish general bounds for the CVaR by assuming bounds over the cumulative distribution functions (CDFs) and probability density functions (PDFs) of the original and simplified models. These bounds are then used to estimate the difference between the value functions of the original and simplified models. The framework includes theoretical performance guarantees for these bounds, ensuring that the simplified model's performance is close to that of the original model, thus enabling efficient evaluation of the value function without real-time access to the computationally expensive model.

Main Finding

The authors discovered that by using a computationally cheaper belief-MDP transition model, they could effectively simplify the evaluation of Conditional Value at Risk (CVaR) in Partially Observable Markov Decision Processes (POMDPs). They established general bounds for CVaR by assuming bounds over the cumulative distribution functions (CDFs) and probability density functions (PDFs) of the original and simplified models. These bounds allowed them to estimate the difference between the value functions of the original and simplified models with high probability. Additionally, they provided theoretical performance guarantees for these bounds, ensuring that the simplified model's performance is close to that of the original model. This framework enables efficient evaluation of the value function without real-time access to the computationally expensive model, making it feasible for real-time deployment of POMDP policies in risk-averse settings.

Conclusion

The conclusion of the paper is that the authors have developed a framework for simplifying the evaluation of Conditional Value at Risk (CVaR) in Partially Observable Markov Decision Processes (POMDPs). This framework involves using a computationally cheaper belief-MDP transition model to replace the original, more complex model. They established general bounds for CVaR and derived theoretical bounds for the value function using the simplified model. The framework includes theoretical performance guarantees, ensuring that the simplified model's performance is close to that of the original model. This allows for efficient evaluation of the value function without real-time access to the computationally expensive model, making it feasible for real-time deployment of POMDP policies in risk-averse settings.

Keywords

POMDP, CVaR, belief-MDP, risk-averse decision-making, computational simplification, value function bounds, performance guarantees, cumulative distribution functions, probability density functions, total variation distance, online deployment, autonomous agents, uncertainty, partial observability.