How do you choose the best reward function for your reinforcement learning problem?

1 Reward function basics

A reward function is a mathematical expression that maps an agent's state and action to a numerical value, called a reward. The reward indicates how desirable or undesirable the agent's behavior is in that situation. The agent's goal is to maximize the total reward it receives over time, by learning a policy that tells it what action to take in each state. A reward function should capture the essence of your RL problem, and align with your desired outcome and constraints.

2 Reward function types

Reward functions vary in terms of how they are defined and delivered. Sparse rewards, for instance, are only given when a specific goal state is reached, like winning a game or completing a task. This type of reward is easy to understand but can be difficult to learn from as the agent must explore many states before finding a positive signal. Dense rewards, on the other hand, are given at every step based on progress or performance measures such as distance to the goal or score. This can help speed up learning as the agent receives more feedback and guidance, but can also lead to bias or distraction if the agent optimizes for the wrong objective or gets stuck in local optima. Lastly, shaped rewards use domain knowledge or heuristics such as potential function or reward shaping to give the agent reward. This type of reward can incorporate prior knowledge or intuition and help the agent learn faster and better, but it may require expert knowledge or careful tuning.

3 Reward function challenges

Designing a good reward function is not easy, as it involves balancing various trade-offs and challenges. Alignment is key, as the reward function should match your true objective and preferences, not incentivize unwanted or harmful behavior. Additionally, the reward function must be able to generalize across different states and scenarios without depending on specific assumptions or conditions. It should also be robust and resistant to noise, errors, or manipulation, so that it cannot be exploited or hacked by the agent. All of these considerations must be taken into account when designing a reward function.

4 Reward function tips

Designing a better reward function to overcome challenges can be achieved by following some tips and best practices. Start with a sparse or binary reward function that is easy to define and understand, then add complexity or refinement as needed. Domain knowledge can also be used to shape or enhance the reward function, but be careful not to overfit or bias it. Test and evaluate the reward function on different settings and metrics, such as learning curves, performance indicators, or behavior patterns. Use techniques such as reward analysis or inverse reinforcement learning to inspect or infer the reward function from the agent's behavior. Iterate and improve your reward function based on results and feedback, or use methods such as reward learning or multi-objective optimization to learn or optimize the reward function from data or preferences until you achieve your desired outcome and satisfaction.

5 Reward function examples

To illustrate some of these concepts and tips, let's look at some examples of reward functions for different RL problems. For the Cartpole problem, a simple reward function is to give +1 for every step that the pole stays upright, and 0 otherwise. This reward function is sparse and binary, which aligns with the goal of keeping the pole balanced. For the Mountain car problem, a simple reward function is to give -1 for every step that the car does not reach the goal, and 0 otherwise. This reward function is sparse and negative, which encourages the agent to reach the goal as fast as possible. Lastly, for Atari games, a common reward function is to use the game score as the reward. This reward function is dense and positive, reflecting the game objective and rules.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?