A2C algorithm in tf.keras: actor loss function

Question

I'm learning about Action-Critic Reinforcement Learning techniques, in particular A2C algorithm.

I've found a good description of a simple version of the algorithm (i.e. without experience replay, batching or other tricks) with implementation here: https://link.medium.com/yi55uKWwV2. The complete code from that article is available on GitHub.

I think I understand ok-ish what's happening here, but to make sure I actually do, I'm trying to reimplement it from scratch using higher-level tf.keras APIs. Where I'm getting stuck is how do I implement training loop correctly, and how do I formulate actor's loss function.

1. What is the correct way to pass action and advantage into the loss function?
2. Actor's loss function involves computing probability of the action taken given to normal distribution. How can I ensure that mu and sigma of the normal distribution during loss function computation actually match the ones were during prediction?
3. The way it is in the original, the actor's loss function doesn't care about y_pred, it only does about action that was chosen while interacting with the environment. This seems to be wrong, but I'm not sure how.

The code I have so far: https://gist.github.com/nevkontakte/beb59f29e0a8152d99003852887e7de7

Edit: I suppose some of my confusion stems from a poor understanding of magic behind gradient computation in Keras/TensorFlow, so any pointers there would be appreciated.

Answer 1

First, credit where credit is due: information provided by ralf htp and Simon was instrumental in helping me to figure out the right answers eventually.

Before I go into detailed answers to my own questions, here's the original code I was trying to rewrite in tf.keras terms, and here's my result.

What is the correct way to pass action and advantage into a loss function in Keras?

There is a difference between what raw TF optimizer considers a loss function and what Keras does. When using an optimizer directly, it simply expects a tensor (lazy or eager depending on your configuration), which will be evaluated under tf.GradientTape() to compute the gradient and update weights.

Example from https://medium.com/@asteinbach/actor-critic-using-deep-rl-continuous-mountain-car-in-tensorflow-4c1fb2110f7c:

# Below norm_dist is the output tensor of the neural network we are training.
loss_actor = -tfc.log(norm_dist.prob(action_placeholder) + 1e-5) * delta_placeholder
training_op_actor = tfc.train.AdamOptimizer(
    lr_actor, name='actor_optimizer').minimize(loss_actor)

# Later, in the training loop...

_, loss_actor_val = sess.run([training_op_actor, loss_actor],
                             feed_dict={action_placeholder: np.squeeze(action),
                                        state_placeholder: scale_state(state),
                                        delta_placeholder: td_error})

In this example it computes the whole graph, including making an inference, capture the gradient and adjust weights. So to pass whatever values you need into the loss function/gradient computation you just pass necessary values into the computation graph.

Keras is a bit more formal in what loss function should look like:

loss: String (name of objective function), objective function or tf.keras.losses.Loss instance. See tf.keras.losses. An objective function is any callable with the signature scalar_loss = fn(y_true, y_pred). If the model has multiple outputs, you can use a different loss on each output by passing a dictionary or a list of losses. The loss value that will be minimized by the model will then be the sum of all individual losses.

Keras will do the inference (forward pass) for you and pass the output into the loss function. The loss function is supposed to do some extra computation on the predicted value and y_true label, and return the result. This whole process will be tracked for the purpose of gradient computation.

Although it is very convenient for traditional training, this is a bit restrictive when we want to pass some extra data in, like TD error. It is possible to work around that and shove all the extra data into y_true, and pull it apart inside the loss function (I found this trick somewhere on the web, but unfortunately lost the link to source).

Here's how I rewrote the above in the end:

def loss(y_true, y_pred):
    action_true = y_true[:, :n_outputs]
    advantage = y_true[:, n_outputs:]
    return -tfc.log(y_pred.prob(action_true) + 1e-5) * advantage

# Below, in the training loop...

# A trick to pass TD error *and* actual action to the loss function: join them into a tensor and split apart
# Inside the loss function.
annotated_action = tf.concat([action, td_error], axis=1)
actor_model.train_on_batch([scale_state(state)], [annotated_action])

Actor's loss function involves computing probability of the action taken given to normal distribution. How can I ensure that mu and sigma of the normal distribution during loss function computation actually match the ones were during prediction?

When I asked this question, I didn't understand well enough how TF compute graph works. So the answer is simple: every time sess.run() is invoked, it must compute the whole graph from scratch. Parameters of the distribution would be the same (or similar) as long as graph inputs (e.g. observed state) and NN weights are the same (or similar).

The way it is in the original, the actor's loss function doesn't care about y_pred, it only does about action that was chosen while interacting with the environment. This seems to be wrong, but I'm not sure how.

What's wrong is the assumption "the actor's loss function doesn't care about y_pred" :) Actor's loss function involves norm_dist (which is action probability distribution), which is effectively an analog of y_pred in this context.

Answer 2

As far as i understand A2C it is the machine learning implementation of activator-inhibitor systems that are also called two-component reaction diffusion systems (https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_system). Activator-inhibitor models are important in any field of science as they describe pattern formations like i.e. the Turing mechanism (simply search the net for activator-inhibitor model and you find a vast amount of information, a very common application are predator-prey models). Also cf the graphic source of graphic : https://www.researchgate.net/figure/Activator-Inhibitor-System_fig1_23671770/

with the explanatory graphic of the A2C algorithm in https://towardsdatascience.com/reinforcement-learning-w-keras-openai-actor-critic-models-f084612cfd69

Activator-inhibitor models are closely linked to the theory of nonlinear dynamical systems (or 'chaos theory') this also becomes obvious in the comparison of the bifurcation tree-like structure in https://medium.com/@asteinbach/rl-introduction-simple-actor-critic-for-continuous-actions-4e22afb712 and the bifurcation tree of a nonlinear dynamical systems like i.e. the logistic map (https://en.wikipedia.org/wiki/Logistic_map, the logistic map is one of the simplest predator-prey models or activator-inhibitor models). Another similarity is the sensitivity to initial condition in A2C models that is described as

This introduces in inherent high variability in log probabilities (log of the policy distribution) and cumulative reward values, because each trajectories during training can deviate from each other at great degrees.

in https://towardsdatascience.com/understanding-actor-critic-methods-931b97b6df3f and the curse of dimensionality appears also in chaos theory, i.e. in attractor reconstruction

From the viewpoint of systems theory the A2C algorithm tries to adapt the initial value (start state) in a way that it ends up at a given endpoint when increasing the growth rate of a dynamical systems i.e. the logistic map (r-value is increased and the initial value (start state) is constantly re-adapted to choose the correct bifurations (actions) in the bifurcation tree )

So A2C tries to numerically solve a chaos theory problem, namely finding the initial value for a given outcome of a nonlinear dynamical system in its chaotic region. Analytically this problem is in most cases not solveable.

The action is the bifurcation points in the bifurcation tree, the states are the future bifurctions.

Both, actions and states, are modeled by two coupled neural networks and this coupling of two neural nets is the great innovation of A2C algorithms.

In https://towardsdatascience.com/reinforcement-learning-w-keras-openai-actor-critic-models-f084612cfd69 is well documented keras code for implementing A2C, so you have a possible implementation there.

The loss function here is defined as the temporal difference (TD) function that is the exact difference between state at the actual bifurcation point and the state at the estimated future one, however this mathematically exactly defined is prone to stochastic error (or noise), so the stochastic error is included in the definition of exact, because in the end machine learning is based on stochastic systems or error calculus, meaning systems that are composed of a deterministic and a stochastic component. To zero this error stochastic gradient descend is used. In keras this is simply implmeneted by choosing optimizer=sge.

This interaction of actual and future step is implemented as memory on https://towardsdatascience.com/reinforcement-learning-w-keras-openai-actor-critic-models-f084612cfd69 in the function remember and this function also links the actor and the critic network (or activator and inhibitor network). This general structure of trial (action), call predict (TD function ), remember and train (i.e. stochastic gradient descent) is fundamental to all reinforcement learning algorithms, and is linked to the structure actual state, action, reward, new state :

The prediction code is also very much the same as it was in previous reinforcement learning algorithms. That is, we just have to iterate through the trial and call predict, remember, and train on the agent:

In the implementation on your first question is solved by applying remember on the critic and the train the critic with these values (this is in the main function), where training always evaluates the loss function, so action and reward are passed to the loss function by remember in this implementation :

   actor_critic.remember(cur_state, action, reward, new_state, done)
   actor_critic.train()

Because of your second question : i am not sure but i think this is achieved by the optimization algorithm (i.e. stochastic gradient descent)

Third question : In the predator-prey model the actors or activator is the prey and the behavior of the prey is only determined by the size or capacity of the habitat (the amount of grass) and the size of the predator (inhibitor) population, so modelling it in this way is consistent with nature or an activator-inhibitor system again. In the main function in https://towardsdatascience.com/reinforcement-learning-w-keras-openai-actor-critic-models-f084612cfd69 also only the critic or inhibitor / predator is trained.