Overfitting Prevention With Minimum Description Length

Wed, 04 Nov 2026 09:00:00 +0800

Minimum description length balances the cost of a model against the data it leaves unexplained

Key Takeaways

An agent that proposes hypotheses and is scored on held-out fit alone drifts toward bloated expressions, because every extra term buys a little fit and costs nothing. That is a property of the objective, not a fault of the agent.
The minimum description length (MDL) principle repairs the objective: score a hypothesis by the bits needed to state it plus the bits needed to encode the data given it. Fit and complexity then share one unit, so the trade-off needs no hand-tuned weight.
Solomonoff induction is the uncomputable ideal behind MDL: weight every hypothesis by two to the power of minus its program length. A two-part code over a restricted expression grammar is the practical approximation.
A complexity charge does not cover search multiplicity. Scoring thousands of candidates against one held-out set leaks information, so a hypothesis scorer also needs a query budget or a fresh holdout per round.

TL;DR

When an LLM (Large Language Model) agent searches a space of candidate rules and is rewarded for held-out fit alone, the winning rule is usually the one with the most free parameters. Minimum description length replaces that reward with a code length, bits for the hypothesis plus bits for the residuals it leaves, which is Occam’s razor stated as an objective. In practice that means parsing each candidate into a restricted expression tree, charging for every node and constant, subtracting the charge from the held-out gain, and bounding how often the holdout may be queried.

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Overfitting Prevention With Minimum Description Length

Key Takeaways

TL;DR