I've been reading about multi-armed bandits and the explore/exploit trade-off that can be solved with dynamic allocation indices such as the Gittins Index Theorem. Could this be applied to when to change investment/trading strategies assuming no cost in switching such strategies? If the fund's risk aversion is an issue, would this be applicable to a risk-neutral actor (say a hedge fund)?
Gittins is as useful as your ability to forecast returns and uncertainty.
Depending on what you use for 'uncertainty,' you may just be replicating processes that other financial metrics already accomplish.
That said, there is nothing wrong with using Gittins to attempt dynamic, tactical asset allocation. It's a matter of how well your forecasting works. You need to forecast returns, and whatever you use for uncertainty, such as expected volatility, expected drawdowns, some other custom function that quantifies the uncertainty input, etc.
If you have several trading strategies that produce consistent risks and have consistent returns that you are comfortable using to forecast, Gittins could be used to help with the timing of a switch between strategies.