Safe Exploration in Finite Markov Decision Processes with Gaussian Processes (1606.04753v2)

Abstract: In classical reinforcement learning, when exploring an environment, agents accept arbitrary short term loss for long term gain. This is infeasible for safety critical applications, such as robotics, where even a single unsafe action may cause system failure. In this paper, we address the problem of safely exploring finite Markov decision processes (MDP). We define safety in terms of an, a priori unknown, safety constraint that depends on states and actions. We aim to explore the MDP under this constraint, assuming that the unknown function satisfies regularity conditions expressed via a Gaussian process prior. We develop a novel algorithm for this task and prove that it is able to completely explore the safely reachable part of the MDP without violating the safety constraint. To achieve this, it cautiously explores safe states and actions in order to gain statistical confidence about the safety of unvisited state-action pairs from noisy observations collected while navigating the environment. Moreover, the algorithm explicitly considers reachability when exploring the MDP, ensuring that it does not get stuck in any state with no safe way out. We demonstrate our method on digital terrain models for the task of exploring an unknown map with a rover.

• The paper introduces SafeMDP, demonstrating that GP-based modeling can safely guide exploration in finite MDPs by avoiding actions that could lead to unsafe states.
• The methodology employs a dual-set strategy to maintain safe states and potential expansions, ensuring agents can always return to safety.
• Empirical results from rover exploration simulations validate that SafeMDP outperforms traditional methods, enhancing both exploration efficiency and safety adherence.

Safe Exploration in Finite Markov Decision Processes with Gaussian Processes

In "Safe Exploration in Finite Markov Decision Processes with Gaussian Processes," the authors propose a novel methodology to address safety concerns in reinforcement learning (RL), specifically within finite Markov Decision Processes (MDPs). Traditional RL algorithms often prioritize learning efficiency, accepting some level of risk in the form of unsafe actions for potential future rewards. However, in safety-critical domains, such as robotics, this risk can lead to catastrophic outcomes. Thus, there is an imperative need for methods that prioritize safety without compromising exploration capabilities.

Theoretical Framework and Methodology

The paper introduces the SafeMDP algorithm, which leverages Gaussian Processes (GPs) to model unknown safety constraints associated with state-action pairs within MDPs. Key advances in this work include:

• Safety Modeling with Gaussian Processes: Safety is defined by an unknown function that associates states and actions to a safety measure. GPs provide a probabilistic framework to learn and infer these safety conditions, accommodating noisy observations from the environment.
• Safe Exploration Strategy: SafeMDP proactively explores the MDP by maintaining two sets: a current safe set of states, $\hat{S}_t$, and a potential expansion set, $G_t$. The method carefully selects actions that maximize information gain regarding the safety of new states while ensuring these selections do not violate known safety constraints.
• Reachability Considerations: A critical component of the SafeMDP algorithm is its consideration of state reachability and returnability. This ensures that the algorithm not only considers a state's immediate safety but also guarantees that an agent can return to a safe region, thereby avoiding dead ends.

The algorithm guarantees that the exploration is both complete and safe. It completely explores the safely reachable region defined by the initial set of safe states, without visiting any unsafe state with high probability. The method carefully balances the exploration-exploitation trade-off by leveraging uncertainty estimates provided by the GP model to confidently expand the safe region.

Empirical Validation

The authors validate their approach with experiments simulating a rover's exploration task on an unknown terrain, emulating a real-world scenario like Mars surface exploration. The experiments demonstrate that SafeMDP can effectively explore large portions of a safely reachable region while avoiding unsafe states and actions, such as entering a crater or climbing overly steep slopes that exceed the rover's capabilities. Compared to baseline methods, SafeMDP shows superior exploration efficiency and safety adherence.

Theoretical Implications

On the theoretical front, the paper extends the application of GPs beyond traditional settings into safe exploration for deterministic, finite MDPs. This is achieved by explicitly incorporating reachability constraints into the exploration process, distinguishing this work from other Bayesian optimization approaches that do not account for sequential decision-making processes inherent in MDPs.

The use of confidence bounds derived from the GP model ensures the algorithm operates within a rigorous probabilistic framework. The paper’s derivation of theoretical guarantees, such as the bounds on exploration efficiency in relation to the GP information capacity, offers a significant contribution to the robust and safe design of RL algorithms.

Practical Implications and Future Directions

From a practical perspective, SafeMDP presents a viable strategy for deploying RL systems in environments where safety is paramount, such as autonomous vehicles, medical robotics, and industrial automation. The integration of GPs allows the algorithm to dynamically adapt to new environments, predicting and avoiding unsafe regions without direct prior knowledge, which is crucial in real-world applications where exhaustive safety pre-mapping is impractical.

Future research could focus on extending this framework to accommodate stochastic dynamics within MDPs, examining the impact of varying noise levels in safety observations, or exploring multi-agent systems where coordination in safe exploration becomes necessary. Additionally, adapting this approach for high-dimensional continuous state-action spaces could further increase its applicability, leveraging advancements in scalable GP methods.

In conclusion, the work of Turchetta, Berkenkamp, and Krause addresses a critical gap in the safe application of reinforcement learning and provides a solid foundation for further exploration of safety in complex decision-making systems.