Thompson Sampling
A Bayesian probability-matching algorithm that balances exploration of uncertain options with exploitation of known winners, commonly used in multi-armed bandit problems and adaptive trading strategy selection.
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Explained Simply
Thompson Sampling is a principled way to solve the explore-exploit dilemma: when should you stick with what's working vs. try something new?
The classic setup: You have N strategies (or slot machines). Each has an unknown true win rate. You want to maximize total wins over time. If you only exploit (always play the currently best-performing strategy), you might miss a better option that hasn't been tried enough. If you always explore (try everything equally), you waste time on clearly inferior options.
Thompson Sampling's elegant solution:
- For each strategy, maintain a probability distribution over its true win rate (a Beta distribution initialized at Beta(1,1) — equal uncertainty)
- Each decision round: sample one value from each strategy's distribution
- Pick the strategy with the highest sampled value
- After observing the outcome, update that strategy's distribution (win: add 1 to alpha; loss: add 1 to beta)
Why it works: Strategies with high uncertainty (few trials) have wide distributions with high variance — they're often sampled high, getting explored. Strategies with consistent wins narrow to high values. Strategies with consistent losses narrow to low values. Over time, allocation naturally concentrates on high performers while never completely abandoning untried options.
Key advantages over simpler approaches:
- No fixed exploration rate to tune (like epsilon-greedy)
- Provably near-optimal regret bounds
- Naturally reduces exploration as more data is collected
- Handles non-stationary environments well with discounting
For trading strategy selection, Thompson Sampling adapts to changing market regimes: if momentum strategies start underperforming (losses → beta increases), they get sampled lower more often, reducing allocation automatically.
Thompson Sampling vs. Other Bandit Algorithms
Epsilon-Greedy: With probability ε, explore randomly; otherwise, exploit the current best. Simple but requires tuning ε — too high wastes time exploring; too low fails to adapt to change.
UCB (Upper Confidence Bound): Choose the option with the highest upper confidence bound (mean + exploration bonus). Deterministic given the same data. Doesn't naturally handle non-stationary environments.
Thompson Sampling: Probabilistic sampling from posterior distributions. No tuning required. Naturally adaptive. Handles non-stationarity with discounting. Computationally cheap for Beta distributions.
For trading strategy selection, Thompson Sampling's natural adaptation to changing market regimes makes it the preferred choice.
How to Use Thompson Sampling
- 1
Understand the Explore-Exploit Tradeoff
Thompson sampling balances exploring (trying different strategies to learn which works best) with exploiting (using the strategy that currently appears best). It samples from probability distributions of each strategy's success rate to decide which to use next.
- 2
Apply to Strategy Selection
Maintain a Beta distribution for each trading strategy based on its win/loss record. Each day, sample from each distribution and use the strategy that draws the highest value. Strategies with high win rates are exploited more; underexplored strategies occasionally get tested.
- 3
Update After Each Trade
After each trade, update the winning strategy's Beta distribution: add 1 to alpha (success parameter) for wins, 1 to beta (failure parameter) for losses. Over time, the distributions narrow and Thompson sampling converges on the best-performing strategy while still occasionally exploring alternatives.
Frequently Asked Questions
How quickly does Thompson Sampling adapt to a regime change?
Adaptation speed depends on the discount factor applied to historical outcomes. With no discounting, older data fully weights newer data. With a 0.9 discount per trade, outcomes from 20 trades ago have only 12% weight. Tradewink uses time-based discounting — outcomes older than 2 weeks are down-weighted, allowing adaptation to weekly regime shifts while still using sufficient historical data.
Can Thompson Sampling be used for parameter optimization too?
Yes — Bayesian optimization (a variant of Thompson Sampling with Gaussian Processes instead of Beta distributions) is widely used for hyperparameter tuning. For continuous parameter spaces (like stop-loss multiplier), you replace the Beta distribution with a Gaussian Process prior.
Does Thompson Sampling require a lot of data to work?
It works from the very first trial — it starts with a uniform prior (equal uncertainty about all strategies) and updates with each observation. It becomes more reliable with more data, but it produces valid allocations even with just a handful of trades per strategy.
How Tradewink Uses Thompson Sampling
Tradewink's `RLStrategySelector` uses Thompson Sampling to adaptively weight intraday strategies (momentum breakout, VWAP mean-reversion, ORB, etc.). Each strategy maintains Beta distribution parameters updated after every trade outcome. The selector samples from each distribution to decide which strategy to prioritize in the current scan cycle. This means strategies that have been performing well recently get higher allocation, while underperforming strategies are naturally de-weighted — without a static schedule or manual tuning. The system also applies time decay to historical outcomes, so a strategy's performance last month matters less than its performance this week.
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See Thompson Sampling in real trade signals
Tradewink uses thompson sampling as part of its AI signal pipeline. Get daily trade ideas with full analysis — free to start.