Discuss the concept of regret in reinforcement learning and its implications on algorithm performance.
Instruction: Describe what regret is in the context of reinforcement learning and how minimizing regret impacts the performance of learning algorithms.
Updated
Example Answer
Regret compares the reward an agent earns with a specified benchmark, such as the best action or policy available in the same environment. I would define that benchmark and horizon before quoting a regret result.
In a stationary bandit, expected pseudo-regret counts how often each suboptimal action is chosen, weighted by its gap from the best action's mean reward. It is an expected opportunity cost, not proof that we observe the unrealized reward of every alternative on each round. In an MDP, actions also change future states, so the appropriate policy benchmark and assumptions are more involved.
Sublinear cumulative regret means average regret decreases with time. Fixed exploration can keep incurring a constant loss per round, giving linear regret even after value estimates are accurate. Bounds for a particular bandit algorithm do not automatically apply to a deep RL agent or a changing environment.
Worked Example
With two bandit arms of means 0.8 and 0.6, choosing the worse arm 100 times produces expected pseudo-regret 100 × 0.2 = 20. With fixed ε = 0.1 and uniform exploratory choices, even an already-correct greedy estimate chooses that arm on about 5% of rounds, adding about 0.01 × T regret.