Why are My Q-Learning Values Exploding?

Q-Learning Values Exceeding Threshold

In your implementation of Q-Learning, you encountered a problem where Q-values grew excessively large, resulting in overflow. To address this, let's examine the fundamental concepts and potential issues:

Reward Function

The provided reward function assigns a positive reward for every time step, promoting long-term play over winning. This is undesirable since the agent should be incentivized to strive for victory.

Update Equation

The crux of the issue lies in the update equation for Q-values:

agent.values[mState] = oldVal + (agent.LearningRate * (agent.prevScore + (agent.DiscountFactor * reward) - oldVal))

Here, agent.prevScore represents the reward from the previous state-action. However, in your implementation, you have it set to the Q-value of the previous step (i.e., oldVal). This mistake leads to an unbounded increase in Q-values.

Solution

After correcting this error by assigning agent.prevScore to the reward from the previous step, the agent's behavior normalizes. The updated Q-values now reflect the expected total reward, incentivizing the agent to pursue victory.

Q-Value Ranges

In typical Q-Learning problems, Q-values are bounded by the maximum possible rewards and penalties. In your case, the reward function limits Q-values to [-1, 1], as it assigns -1 for a loss and 1 for a win. However, in other scenarios, the range may be larger or even unbounded. The expected total reward is a critical factor in determining the range of Q-values.

By addressing these issues, you have successfully implemented Q-Learning and can now train an agent that plays in a more strategic manner, prioritizing winning over prolonged play.

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