Minimax Optimality and Spectral Routing for Majority-Vote Ensembles under Markov Dependence

• URL: http://arxiv.org/abs/2604.13414v1
• Date: Wed, 15 Apr 2026 02:32:30 GMT
• Title: Minimax Optimality and Spectral Routing for Majority-Vote Ensembles under Markov Dependence
• Abstract summary: Majority-vote ensembles achieve variance reduction by averaging over diverse, approximately independent base learners.<n>We provide a minimax characterization of this phenomenon for discrete classification in a fixed-dimensional Markov setting.<n>Experiments on synthetic Markov chains, 2D spatial grids, the 128-dataset UCR archive, and Atari DQN ensembles validate the theoretical predictions.
• Score: 6.908972852063454
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Majority-vote ensembles achieve variance reduction by averaging over diverse, approximately independent base learners. When training data exhibits Markov dependence, as in time-series forecasting, reinforcement learning (RL) replay buffers, and spatial grids, this classical guarantee degrades in ways that existing theory does not fully quantify. We provide a minimax characterization of this phenomenon for discrete classification in a fixed-dimensional Markov setting, together with an adaptive algorithm that matches the rate on a graph-regular subclass. We first establish an information-theoretic lower bound for stationary, reversible, geometrically ergodic chains in fixed ambient dimension, showing that no measurable estimator can achieve excess classification risk better than $Ω(\sqrt{\Tmix/n})$. We then prove that, on the AR(1) witness subclass underlying the lower-bound construction, dependence-agnostic uniform bagging is provably suboptimal with excess risk bounded below by $Ω(\Tmix/\sqrt{n})$, exhibiting a $\sqrt{\Tmix}$ algorithmic gap. Finally, we propose \emph{adaptive spectral routing}, which partitions the training data via the empirical Fiedler eigenvector of a dependency graph and achieves the minimax rate $\mathcal{O}(\sqrt{\Tmix/n})$ up to a lower-order geometric cut term on a graph-regular subclass, without knowledge of $\Tmix$. Experiments on synthetic Markov chains, 2D spatial grids, the 128-dataset UCR archive, and Atari DQN ensembles validate the theoretical predictions. Consequences for deep RL target variance, scalability via Nyström approximation, and bounded non-stationarity are developed as supporting material in the appendix.

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