Reinforcement Learning with Lookahead Information (2406.02258v2)

Abstract: We study reinforcement learning (RL) problems in which agents observe the reward or transition realizations at their current state before deciding which action to take. Such observations are available in many applications, including transactions, navigation and more. When the environment is known, previous work shows that this lookahead information can drastically increase the collected reward. However, outside of specific applications, existing approaches for interacting with unknown environments are not well-adapted to these observations. In this work, we close this gap and design provably-efficient learning algorithms able to incorporate lookahead information. To achieve this, we perform planning using the empirical distribution of the reward and transition observations, in contrast to vanilla approaches that only rely on estimated expectations. We prove that our algorithms achieve tight regret versus a baseline that also has access to lookahead information - linearly increasing the amount of collected reward compared to agents that cannot handle lookahead information.

• The paper presents dynamic programming approaches that extend Bellman equations to incorporate lookahead rewards and transitions for enhanced decision-making.
• The paper develops two Monotonic Value Propagation variants, MVP-RL and MVP-TL, achieving provable regret bounds of O(√(H³SAK) ln(SAHK/δ)) and O(√(H²SK)(√H+√A) ln(SAHK/δ)) respectively.
• The paper proposes novel techniques such as variance-based transition bonuses and list representations, opening avenues for multi-step lookahead and model-free RL applications.

Reinforcement Learning with Lookahead Information

This paper provides a detailed exploration of Reinforcement Learning (RL) where agents are endowed with lookahead information, specifically on rewards or transitions, before executing their actions. Such scenarios are prevalent in various practical applications, including financial transactions and navigation. The work highlights that traditional RL methods, which typically optimize expected rewards based on past observations, may not capitalize on lookahead information. The paper addresses this by devising new learning algorithms that effectively incorporate such information, achieving provable efficiency in unknown environments.

Key Contributions

The paper's main contributions are twofold:

1. Dynamic Programming for Lookahead Information: The authors derive BeLLMan equations tailored to RL settings with lookahead information, allowing the formulation of optimal policies and values. The extended MDP formulations, namely $M^R$ for reward lookahead and $M^T$ for transition lookahead, embed reward and transition observations into the state space. This transformation enables the application of standard RL techniques to these augmented MDPs.
2. Provably-Efficient Algorithms:

The paper introduces two variants of the Monotonic Value Propagation (MVP) algorithm: - MVP-RL for Reward Lookahead:

Formulating the policy and planning procedure using the empirical distribution of reward observations. The algorithm achieves a regret bound of $O(\sqrt{H^3SAK}\ln\frac{SAHK}{\delta})$, matching the lower bound for episodic RL. - MVP-TL for Transition Lookahead:

Integrating one-step transition observations into planning and policy formulation. The regret for this algorithm is bounded by $$O(\sqrt{H^2SK}(\sqrt{H}+\sqrt{A})\ln\frac{SAHK}{\delta})$$, accommodating the increase in state-action space due to lookahead transitions.

Experimental Results and Implications

The algorithms demonstrate tight regret bounds when compared to agents that leverage the same lookahead information. This validates the theoretical assertions and shows practical improvements in cumulative rewards collected by agents. The empirical results underscore the potential of lookahead information in improving decision-making and efficiency in RL tasks.

Theoretical Insights and Novel Techniques

The paper also introduces several novel techniques and theoretical insights:

• Variance-based Transition Bonuses:

The value iteration in MVP-TL incorporates bonuses that account for the empirical variance of planned values, providing tighter bounds on the expected values’ deviation from the true values.

• List Representations:

For transition lookahead, the value functions are efficiently computed using list representations of next-state-action pairs, simplifying the complexity of possible state transitions.

Discussion and Future Directions

The research opens several avenues for further exploration:

• Multi-step Lookahead:

Extending the algorithms to handle multi-step lookahead information, where agents foresee multiple steps ahead, poses an interesting challenge.

• Model-free Algorithms:

Developing model-free RL algorithms that integrate lookahead information could enhance computational efficiency.

• Applications in Complex Domains:

Applying these algorithms to more complex domains such as linear MDPs and scenarios with noisy or budget-constrained lookahead information can validate and extend their utility.

Conclusion

In conclusion, this paper makes significant strides in bridging the gap between traditional RL methods and the potential of lookahead information. By embedding immediate observations into the learning process, the proposed algorithms achieve substantial improvements in reward collection and set the stage for a new class of RL methods capable of leveraging anticipatory insights. These advancements not only present strong theoretical foundations but also bear promising implications for the future of RL in dynamic and uncertain environments.