What is the difference between deterministic and stochastic policies?

A deterministic policy is a decision-making rule that always selects the same action for a given state. In reinforcement learning, this means the policy directly maps a state to a single action, like a function action = policy(state). For example, a robot navigating a grid might always move right when in a specific cell. Deterministic policies are straightforward to implement and debug because their behavior is predictable. They’re often used in controlled environments where randomness isn’t needed, such as industrial automation or scripted game AI. However, deterministic policies can struggle in uncertain environments where exploration or adaptability is required.

A stochastic policy, in contrast, assigns probabilities to actions for a given state. Instead of a single action, the policy outputs a distribution, like P(action | state), which defines the likelihood of each possible action. For instance, a self-driving car might have a 60% chance to accelerate and 40% to brake in a specific scenario. Stochastic policies are useful for exploration in reinforcement learning, as they allow agents to try different actions and discover optimal strategies. They’re also robust to partial observability—if a state’s information is incomplete, randomness can help avoid getting stuck in suboptimal patterns. However, stochastic policies require managing probability distributions, which adds complexity to training and implementation.

The key difference lies in how actions are chosen. Deterministic policies are rigid but efficient, while stochastic policies trade predictability for flexibility. For example, in game AI, a deterministic policy might always attack an enemy from the left, making it exploitable by opponents. A stochastic policy could randomize attack directions, making the AI harder to predict. Developers might choose deterministic policies for tasks requiring consistency (e.g., robotic assembly lines) and stochastic ones for tasks needing exploration (e.g., training an agent to play poker). Implementation-wise, deterministic policies are simpler to code (e.g., lookup tables), while stochastic policies often require frameworks that handle probability sampling, like PyTorch’s torch.distributions or TensorFlow’s probability layers.