Let’s briefly look at how RL works. Suppose we are given some environment (e.g. a game) that we’d like to train an agent on. To describe the behavior of the agent, we define a policy function (the brain of the agent), which computes how the agent should act in any given situation. In practice, the policy is usually a neural network that takes the current state of the game as an input and calculates the probability of taking any of the allowed actions. A typical policy function might have about 1,000,000 parameters, so our task comes down to finding the precise setting of these parameters such that the policy plays well (i.e. wins a lot of games).

The training process for the policy works as follows. Starting from a random initialization, we let the agent interact with the environment for a while and collect episodes of interaction (e.g. each episode is one game of Pong). We thus obtain a complete recording of what happened: what sequence of states we encountered, what actions we took in each state, and what the reward was at each step. As an example, below is a diagram of three episodes that each took 10 time steps in a hypothetical environment. Each rectangle is a state, and rectangles are colored green if the reward was positive (e.g. we just got the ball past our opponent) and red if the reward was negative (e.g. we missed the ball):

On “Evolution”. Before we dive into the ES approach, it is important to note that despite the word “evolution”, ES has very little to do with biological evolution. Early versions of these techniques may have been inspired by biological evolution and the approach can, on an abstract level, be seen as sampling a population of individuals and allowing the successful individuals to dictate the distribution of future generations. However, the mathematical details are so heavily abstracted away from biological evolution that it is best to think of ES as simply a class of black-box stochastic optimization techniques.

Black-box optimization. In ES, we forget entirely that there is an agent, an environment, that there are neural networks involved, or that interactions take place over time, etc. The whole setup is that 1,000,000 numbers (which happen to describe the parameters of the policy network) go in, 1 number comes out (the total reward), and we want to find the best setting of the 1,000,000 numbers. Mathematically, we would say that we are optimizing a function f(w) with respect to the input vector w (the parameters / weights of the network), but we make no assumptions about the structure of f, except that we can evaluate it (hence “black box”).

The ES algorithm. Intuitively, the optimization is a “guess and check” process, where we start with some random parameters and then repeatedly 1) tweak the guess a bit randomly, and 2) move our guess slightly towards whatever tweaks worked better. Concretely, at each step we take a parameter vector w and generate a population of, say, 100 slightly different parameter vectors w1 ... w100 by jittering w with gaussian noise. We then evaluate each one of the 100 candidates independently by running the corresponding policy network in the environment for a while, and add up all the rewards in each case. The updated parameter vector then becomes the weighted sum of the 100 vectors, where each weight is proportional to the total reward (i.e. we want the more successful candidates to have a higher weight). Mathematically, you’ll notice that this is also equivalent to estimating the gradient of the expected reward in the parameter space using finite differences, except we only do it along 100 random directions. Yet another way to see it is that we’re still doing RL (Policy Gradients, or REINFORCE⁠(opens in a new window) specifically), where the agent’s actions are to emit entire parameter vectors using a gaussian policy.

Injecting noise in the parameters. Notice that the objective is identical to the one that RL optimizes: the expected reward. However, RL injects noise in the action space and uses backpropagation to compute the parameter updates, while ES injects noise directly in the parameter space. Another way to describe this is that RL is a “guess and check” on actions, while ES is a “guess and check” on parameters. Since we’re injecting noise in the parameters, it is possible to use deterministic policies (and we do, in our experiments). It is also possible to add noise in both actions and parameters to potentially combine the two approaches.