Bandit based yield theory is a branch of economics that deals with the problem of how to optimally allocate resources when there is uncertainty about the returns on different investments. The term “bandit” refers to the fact that there is an element of risk involved in these investments, as there is a chance that the returns will be lower than expected or that the investment will fail entirely.
At its core, bandit based yield theory is concerned with finding the optimal balance between exploration and exploitation. Exploration refers to the process of trying out new investments or strategies in order to learn more about their potential returns. Exploitation, on the other hand, involves sticking with what has been proven to be successful in the past and maximizing the returns from those investments.
The problem with exploration is that it can be risky and costly, as there is no guarantee that the new investments will be successful. On the other hand, if an investor only focuses on exploitation, they may miss out on potential opportunities for higher returns. The goal of bandit based yield theory is to find the optimal balance between these two conflicting objectives.
One of the key concepts in bandit based yield theory is the concept of the “multi-armed bandit”. This refers to a situation where an investor has a number of different investments to choose from, each with its own potential returns and risks. The investor must decide which investments to pursue in order to maximize their overall returns, while also taking into account the level of risk involved in each investment.
One approach to solving the multi-armed bandit problem is the “explore-then-commit” strategy, which involves initially exploring a number of different investments in order to gather information about their potential returns. Once the investor has gathered enough information, they can then commit to the investment with the highest expected return.
Another approach is the “optimistic initial values” strategy, which involves initially assigning high expected returns to all investments, even if there is little information available about them. This encourages the investor to explore more investments in order to gather information and improve their estimates of the expected returns.
A third approach is the “UCB1” (Upper Confidence Bound) algorithm, which involves assigning a confidence interval to each investment based on the amount of information available about it. The investor then chooses the investment with the highest upper confidence bound, as this represents the investment with the highest expected return given the current level of information.
One of the key benefits of bandit based yield theory is that it allows investors to adapt to changing market conditions and adjust their investment strategies accordingly. For example, if an investor is using the explore-then-commit strategy and discovers that an investment has much lower returns than expected, they can adjust their strategy and explore other investments instead.
There are also a number of variations and extensions to bandit based yield theory that have been developed in order to address more complex situations. One example is the “multi-armed bandit with switching costs” model, which takes into account the fact that switching between investments can be costly in terms of time and resources. This model helps investors to determine when it is worth switching investments and when it is better to stick with what they have.
Another extension is the “stochastic multi-armed bandit” model, which deals with situations where the returns on investments are not fixed, but rather vary randomly over time. This model helps investors to determine the optimal investment strategy in such situations, taking into account the level of uncertainty and the expected returns.