I run a research lab that tests genetic-algorithm offspring against historical market regimes. Every (gene, regime) cell I evaluate burns CPU and wall-clock time. The grid is large enough that I cannot test everything, but I need to allocate tests in a way that actually learns the map instead of getting stuck in one corner of it.
That makes it a bandit problem. The arm is "test this gene in this regime." The reward is the validated deflated Sharpe, after fees, after walk-forward folds. And like every real bandit problem, the arms are not independent. Neighboring cells share information.
I considered three policies before picking one.
Epsilon-greedy. Simple, but it explores indiscriminately. With a large grid, most random pulls land on cells I already know are dead. I would waste budget on regions the posterior already rules out.
UCB. Better. It explicitly trades off mean and uncertainty. But UCB's optimism is deterministic given the visit count. Two cells with identical visits and identical observed means get identical scores, even when one sits next to a high-yield cluster. To get information-sharing across cells I would have to bolt a contextual model on top, and at that point UCB's clean theoretical guarantees stop holding anyway.
Thompson Sampling. Sample a posterior reward for each candidate cell, then pull the argmax. The randomness comes from the posterior, not from a knob. Two cells with the same observed mean but different variance get different draws on different rounds. And critically: if I model the reward surface as a Gaussian Process over (gene-features, regime-features), one observation updates the posterior for every nearby cell. Information sharing falls out for free.
That last property is why I picked it.
The reward model. For each (gene, regime) cell I track a posterior over expected deflated Sharpe. Prior is centered slightly negative. Most strategies lose money after fees, and I want the system to assume noise until proven otherwise. The likelihood is Gaussian with variance scaled by the number of walk-forward folds completed. The GP kernel uses two feature sets: gene-side features (indicator family, holding period, trade frequency band) and regime-side features (vol bucket, trend score, liquidity regime).
Cold start. New regimes are the hard part. The first time a 2022-style liquidity drought shows up in the grid, the posterior over every cell in that column is just the prior. Thompson Sampling handles this gracefully. High uncertainty means high sample variance means more draws on that column in the next few rounds, automatically. I do not need a special "new regime" rule.
The escape hatch I worried about. Pure TS can starve a cell that got an unlucky early draw. With a tight Gaussian likelihood and small N, one bad observation can push the posterior far enough that the cell almost never gets sampled again. I am mitigating this by capping how confident the posterior is allowed to get with fewer than 8 walk-forward folds. Below that cap, variance stays inflated. It is a Bayesian-flavored hack, but it matches how much I actually trust 4-fold data, which is to say not much.
What I am watching. Three things, over the first month of live operation:
- Coverage entropy across the grid. If TS collapses into a small set of cells, either the prior was too aggressive or the kernel is over-smoothing and faking certainty it has not earned.
- Hit rate of "promoted" cells in held-out regimes. If TS finds clusters that do not generalize, the regime features are the wrong axis and the GP is fitting to noise that happens to cluster in feature space.
- Cost per validated strategy. The whole point is to spend fewer CPU-hours per accepted gene than my old grid-search policy did. If that number does not fall, the policy is not paying for itself regardless of how elegant the math is.
If any of those three break, I will write the postmortem rather than the victory lap.
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