Research map / Multi-agent systems and games / Human-AI and goal-conditioned
Plasticity as the Mirror of Empowerment
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Defines agent plasticity as generalized directed information from observations to actions over arbitrary intervals, shows it mirrors empowerment, and proves a tight plasticity-empowerment tradeoff bound.
Problem
Plasticity (how much an agent's behavior can be influenced by what it observes) has been studied in neuroscience, biology, and ML but lacks a universal, agent-centric information-theoretic definition connected to empowerment.
Approach
Introduces generalized directed information (GDI), which extends directed information to arbitrary-length, non-aligned intervals; defines plasticity as the max over environments of GDI from observations to actions, showing plasticity and empowerment are the same measure with reversed direction, and deriving a tight upper bound on their sum.
Key results
- Plasticity-empowerment tension: E + P <= m = min{(b-a+1) log|O|, (d-c+1) log|A|}, shown tight.
- In a Q-learning bandit experiment, plasticity decreases to zero as epsilon goes from 0 to 1 (epsilon-greedy).
- Empowerment tends to exceed plasticity in the bandit experiment and increases with optimistic initial Q values.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase ε in ε-greedy exploration from 0 toward 1 | Tabular Q-learning · Two-armed Bernoulli bandit, intervals [1:3] and [2:5] | plasticity | Hurt |
| Set ε to 1 instead of relying on the greedy policy | Tabular Q-learning · Two-armed Bernoulli bandit, intervals [1:3] and [2:5] | plasticity | Hurt |
| Increase the initial Q value toward optimism | Tabular Q-learning · Two-armed Bernoulli bandit, intervals [1:3] and [2:5] | empowerment | Helped |
| Use pessimistic initial Q values below zero rather than optimistic values | Tabular Q-learning · Two-armed Bernoulli bandit, intervals [1:3] and [2:5] | empowerment | Hurt |
| Compare estimated plasticity plus empowerment with the theoretical upper bound | Tabular Q-learning · Two-armed Bernoulli bandit, intervals [1:3] and [2:5] | plasticity + empowerment | No clear effect |
Surprising findings
- Every deterministic environment forces zero plasticity for every agent.
Limitations
- Desiderata fall short of a complete axiomatic characterization of plasticity
- Plasticity is defined over behavior (actions), not internal state or synaptic plasticity
- Goals are not incorporated into the framework
Experimental setup
Benchmarks: two-armed Bernoulli bandit
Metrics: plasticity estimate empowerment estimate mutual information
Baselines: Q-learning UCB1
Builds on: directed information empowerment general reinforcement learning
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