A Bellman Optimality Equation for Plasticity
The paper addresses the optimization of plasticity in continual reinforcement learning, a previously unexplored area under the Abel et al. (2025) formalization Plasticity is defined as generalized directed information from an agent's observations to its actions, while empowerment is defined in the reverse direction The authors derive a Bellman optimality equation for optimizing plasticity within Markov decision processes, paralleling existing work on empowerment This work reframes the classical
Analysis
TL;DR
- The paper addresses the optimization of plasticity in continual reinforcement learning, a previously unexplored area under the Abel et al. (2025) formalization
- Plasticity is defined as generalized directed information from an agent's observations to its actions, while empowerment is defined in the reverse direction
- The authors derive a Bellman optimality equation for optimizing plasticity within Markov decision processes, paralleling existing work on empowerment
- This work reframes the classical stability-plasticity dilemma as an empowerment-plasticity tradeoff, providing a unified theoretical framework
- The paper represents preliminary theoretical work establishing the mathematical foundation for plasticity optimization in RL
Why It Matters
This research fills a critical theoretical gap in continual reinforcement learning by providing the first formal treatment of plasticity optimization under the empowerment-plasticity framework. For AI practitioners building agents that must learn continuously without catastrophic forgetting, this work offers a principled mathematical foundation for balancing adaptability against stability. The Bellman equation derivation enables practical algorithm development for lifelong learning systems.
Technical Details
- Builds on Abel et al. (2025)'s information-theoretic formalization where plasticity = generalized directed information from observations to actions, and empowerment = generalized directed information from actions to observations
- Derives a Bellman optimality equation specifically for plasticity optimization within the Markov decision process (MDP) framework
- The derived equation mirrors the structure of existing Bellman equations for empowerment optimization, suggesting a symmetric theoretical treatment of both quantities
- Published as preliminary work on arXiv (2609.10776) by Jeremy Lucas and Doina Precup, submitted September 9, 2026
- Categorized under Machine Learning (cs.LG)
Industry Insight
- The empowerment-plasticity framework could become a foundational paradigm for designing continual learning agents, particularly in robotics and autonomous systems where adaptation without forgetting is essential
- Researchers should monitor follow-up work that may produce practical algorithms from this theoretical foundation, as the Bellman equation derivation opens the door to value-function-based plasticity optimization
- The symmetry between empowerment and plasticity equations suggests potential for unified algorithms that jointly optimize both, offering a more complete solution to the stability-plasticity dilemma in production RL systems
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