Confidence Sequences for Online Statistical Model C... | AI Research

Key Takeaways

Confidence Sequences for Online Statistical Model Checking of Markov Decision Processes Markov Decision Processes (MDPs) are essential for modeling systems t...
Markov decision processes (MDPs) are a classic model of decision making under uncertainty, exhibiting both non-deterministic choice as well as probabilistic uncertainty.
Traditionally, exact knowledge of the underlying probabilities is assumed.
However, this often is unrealistic, e.g.\ when modelling cyber-physical systems or biological processes.
Here, statistical methods provide a way towards obtaining meaningful guarantees.

Paper AbstractExpand

Markov decision processes (MDPs) are a classic model of decision making under uncertainty, exhibiting both non-deterministic choice as well as probabilistic uncertainty. Traditionally, exact knowledge of the underlying probabilities is assumed. However, this often is unrealistic, e.g.\ when modelling cyber-physical systems or biological processes. Here, statistical methods provide a way towards obtaining meaningful guarantees. The classical approach is to gather samples in the MDP, use these to draw statistical conclusions about the transition probabilities, and from there obtain bounds on the true value; then, if these bounds are too broad, repeat. However, existing implementations of this approach are either subtly incorrect or sub-optimal, and quite often both. We present several \emph{confidence sequences}, which are specifically designed for such \enquote{online} settings, implement all of them in an efficient tool, and show their practical applicability. In particular, we show that they outperform classical \enquote{union-bound} style approaches, and overall our implementation requires 50x less samples on average than previous state of the art.

Confidence Sequences for Online Statistical Model Checking of Markov Decision Processes

Markov Decision Processes (MDPs) are essential for modeling systems that involve both decision-making and uncertainty, such as biological processes or cyber-physical systems. While these models are powerful, they often rely on the assumption that we have perfect knowledge of underlying probabilities—an assumption that is rarely true in real-world scenarios. This paper addresses the challenge of verifying these systems when probabilities are unknown by using statistical methods to gather samples and establish reliable bounds on system behavior.

The Problem with Traditional Approaches

In standard statistical model checking, researchers collect samples from an MDP to estimate transition probabilities and calculate performance bounds. If these bounds are too wide to be useful, the process is repeated. The authors identify that current implementations of this method are often either mathematically incorrect or inefficient. Specifically, many existing approaches rely on "union-bound" techniques, which tend to be overly conservative and require a large number of samples to reach a meaningful conclusion.

Introducing Confidence Sequences

To solve these inefficiencies, the authors introduce "confidence sequences," which are statistical tools specifically designed for online settings. Unlike traditional static bounds, confidence sequences are built to provide valid, continuous updates as more data is collected. By integrating these sequences into an efficient software tool, the researchers provide a more robust way to perform statistical model checking without the pitfalls of previous methods.

Significant Performance Gains

The practical impact of this research is substantial. By replacing traditional union-bound approaches with their new confidence sequences, the authors demonstrate a major improvement in efficiency. Their implementation requires, on average, 50 times fewer samples than the current state-of-the-art methods. This reduction in sample size makes the verification of complex MDPs significantly more feasible, allowing for faster and more accurate analysis of systems where exact probabilities are not known from the start.