Contextual bandits face two problems that are usually treated as separate. The first is fitting: estimating the reward of each action from noisy data without overfitting. The second is exploring: ensuring enough variety in chosen actions to improve future estimates. Standard approaches solve them with separate mechanisms — regularization for fitting, Thompson Sampling or epsilon-greedy for exploration. The fitting noise and the exploration noise are different budgets, managed independently.
Li, Casanova, Schwartz, Kostyuk, Kong, and Williams (arXiv:2603.11276, 2026) show that regularization and exploration are the same operation. Cross-validation-based regularization introduces stochasticity into model parameters: different CV folds select different regularization strengths, which produce different parameter estimates, which lead to different action selections. This stochasticity has exactly the right structure to serve as exploration. In the two-armed bandit case, the equivalence is exact — the variation induced by cross-validated regularization is mathematically equivalent to Thompson Sampling.
The RIE-Greedy algorithm exploits this by running a pure greedy policy on a regularized model. No explicit exploration mechanism is added. The agent always picks the action its model estimates as best. But because the model is re-regularized on each round (with different CV splits), the “best” action fluctuates — and the fluctuation pattern automatically concentrates exploration on uncertain actions, exactly as Thompson Sampling would.
This is not a coincidence. Regularization penalizes parameter confidence. Thompson Sampling samples from parameter uncertainty. Both respond to the same underlying quantity — how much the data constrains the parameter estimate — and both produce wider exploration where constraints are weaker. The reason they have always been implemented separately is that they were framed in different vocabularies: regularization belongs to statistical learning theory; Thompson Sampling belongs to decision theory. The shared structure was obscured by the disciplinary boundary.
The practical consequence is that any system already performing cross-validated regularization is already exploring. Adding an explicit exploration mechanism on top is not just redundant — it may be counterproductive, introducing more variance than the problem requires. The noise that prevents overfitting is the noise that discovers new information. One budget, not two.