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Efficient Inverse Multiagent Learning
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Formulates inverse Nash equilibrium and simulacral learning as min-max (generative-adversarial) problems and gives polynomial-time gradient descent ascent methods for exact and stochastic oracles, applied to Spanish electricity price prediction.
Problem
Inferring payoff-function parameters for which observed strategies (or sampled histories of play in Markov games) form a Nash equilibrium, i.e., inverse game theory and inverse multiagent (reinforcement) learning, including simulacra that replicate observations in expectation.
Approach
Cast inverse Nash equilibrium as a zero-sum min-max problem where the stabilizer picks parameters and the destabilizer picks deviations maximizing cumulative regret; under convex-regret and concavity assumptions this is convex-concave (or convex-gradient-dominated for Markov games), so gradient descent ascent finds inverse equilibria in polynomial time, extended to simulacra with observation distr
Key results
- Proposed approach outperforms the widely-used ARIMA method in predicting prices in Spanish electricity markets from time-series data.
- Under convex-regret and concave-game assumptions, the set of inverse Nash equilibria is convex and computable via gradient descent ascent in O(1/epsilon^2) iterations (O(1/epsilon) with extragradient or optimistic GDA).
Surprising findings
- The set of inverse Nash equilibria can be convex even when the set of Nash equilibria is not.
Experimental setup
Datasets: Spanish electricity market price time-series data
Benchmarks: Spanish electricity market prices
Metrics: price prediction accuracy
Baselines: ARIMA
Builds on: maximum entropy inverse reinforcement learning multiagent apprenticeship learning extragradient / optimistic gradient descent ascent
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