Solomonoff induction frames prediction as a mixture over computable hypotheses, typically leading to identification of the true environment.
In a finite meta-reinforcement learning setting with nested constraint families, in our previous work, we observe a different regime: a value-mixture (VM) agent achieves near-optimal, zero-collision navigation without identifying the true environment, a phenomenon we call Free Inference.
This regime persists up to a sharp density threshold, beyond which performance degrades and posterior-mode selection (PMS) becomes preferable.
We formalize this behavior via the Free Inference dimension dFI(S,N), a combinatorial measure of the environmental complexity a VM agent can handle while preserving trajectory coherence.
We prove dFI is strictly smaller than the VC-dimension and relates to the Natarajan dimension up to a path-length factor, capturing the cost of non-decomposable loss.
A PAC-style relaxation yields generalization bounds driven by dFI^(epsilon,delta).
We also define a complementary PMS identification dimension and show that a hybrid strategy---averaging until the first collision, then switching to selection---is optimal, with links to Littlestone-type dimensions supported by grid-world experiments.