In general, model-based reinforcement learning consists of two main parts: learning a dynamics function to model observed state transitions, and then using predictions from that model in some way to decide what to do (e.g., use model predictions to learn a policy, or use model predictions directly in an optimization setup to maximize predicted rewards).

In this assignment, you will do the latter. You will implement both the process of learning a dynamics model, as well as the process of creating a controller to perform action selection through the use of these model predictions. For references to this type of approach, see this paper and this paper.

2 Model-Based Reinforcement Learning

We will now provide a brief overview of model-based reinforcement learning (MBRL), and the specific type of MBRL you will be implementing in this homework. Please see Lecture 11: Model-Based Reinforcement Learning (with specific emphasis on the slides near page 9) for additional details.

MBRL consists primarily of two aspects: (1) learning a dynamics model and (2) using the learned dynamics models to plan and execute actions that minimize a cost function (or maximize a reward function).

2.1 Dynamics Model

In this assignment, you will learn a neural network dynamics model fθ of the form

                                                              ∆ˆ t+1 = fθ(st,at)                                                        (1)

which predicts the change in state given the current state and action. So given the prediction ∆ˆ t+1, you can generate the next prediction with

                                                             ˆst+1 = st + ∆ˆ t+1.                                                       (2)

See the previously referenced paper for intuition on why we might want our network to predict state differences, instead of directly predicting next state.

You will train fθ in a standard supervised learning setup, by performing gradient descent on the following objective:

L(θ) = X k(st+1 −st) − fθ(st,at)k22

(st,at,st+1)∈D

(3)

= X

(4)

(st,at,st+1)∈D

In practice, it’s helpful to normalize the target of a neural network. So in the code, we’ll train the network to predict a normalized version of the change in state, as in

                                L(θ) = X kNormalize(s.                           (5)

(st,at,st+1)∈D

Since fθ is trained to predict the normalized state difference, you generate the next prediction with

                                             ˆst+1 = st + Unnormalize(fθ(st,at)).                                       (6)

2.2 Action Selection

Given the learned dynamics model, we now want to select and execute actions that minimize a known cost function (or maximize a known reward function). Ideally, you would calculate these actions by solving the following optimization:

∞

                           a∗t = argminXc(ˆst0,at0) where ˆst0+1 = ˆst0 + fθ(ˆst0,at0).                      (7)

at:∞ t0=t

However, solving Eqn. 7 is impractical for two reasons: (1) planning over an infinite sequence of actions is impossible and (2) the learned dynamics model is imperfect, so using it to plan in such an open-loop manner will lead to accumulating errors over time and planning far into the future will become very inaccurate.

Instead, one alternative is to solve the following gradient-free optimization problem:

t+H−1

       A∗ = arg                          min X c(ˆst0,at0) s.t. ˆst0+1 = ˆst0 + fθ(ˆst0,at0),                    (8)

{A(0),...,A(K−1)} t0=t

in which A) are each a random action sequence of length

H. What Eqn. 8 says is to consider K random action sequences of length H, predict the result (i.e., future states) of taking each of these action sequences using the learned dynamics model fθ, evaluate the cost/reward associated with each candidate action sequence, and select the best action sequence. Note that this approach only plans H steps into the future, which is desirable because it prevent accumulating model error, but is also limited because it may not be sufficient for solving long-horizon tasks.

A better alternative to this random-shooting optimization approach is the crossen tropy method (CEM), which is similar to random-shooting, but with iterative improvement of the distribution of actions that are sampled from. We first randomly initialize a set of K action sequences A(0),...,A(K−1), like in random shooting. Then, we choose the J sequences with the highest predicted sum of discounted rewards as the ”elite” action sequences. We then fit a diagonal Gaussian with the same mean and variance as the ”elite” action sequences, and use this as our action sampling distribution for the next iteration. After repeating this process M times, we take the final mean of the Gaussian as the optimized action sequence. See Section 3.3 in this paper for more details.

Additionally, since our model is imperfect and things will never go perfectly according to plan, we adopt a model predictive control (MPC) approach, where at every time step we perform random-shooting or CEM to select the best H-step action sequence, but then we execute only the first action from that sequence before replanning again at the next time step using updated state information. This reduces the effect of compounding errors when using our approximate dynamics model to plan too far into the future.

2.3 On-Policy Data Collection

Although MBRL is in theory off-policy—meaning it can learn from any data—in practice it will perform poorly if you don’t have on-policy data. In other words, if a model is trained on only randomly-collected data, it will (in most cases) be insufficient to describe the parts of the state space that we may actually care about. We can therefore use on-policy data collection in an iterative algorithm to improve overall task performance. This is summarized as follows:

2.4 Ensembles

A simple and effective way to improve predictions is to use an ensemble of models. The idea is simple: rather than training one network fθ to make predictions, we’ll train N independently initialized networks, and average their predictions to get your final predictions

In this assignment, you’ll train an ensemble of networks and compare how different values of N effect the model’s performance.

3 Code

You will implement the MBRL algorithm described in the previous section.

3.1 Overview

Obtain the code from https://github.com/berkeleydeeprlcourse/ homework_fall2021/tree/master/hw4.

You will add code to the following three files: agents/mb_agent.py, models/ff_model.py, and policies/MPC_policy.py. You will also need to edit these files by copying code from past homeworks or Piazza: infrastructure/rl_trainer.py and infrastructure/utils.py.

Problem 1

What you will implement:

Collect a large dataset by executing random actions. Train a neural network dynamics model on this fixed dataset and visualize the resulting predictions. The implementation that you will do here will be for training the dynamics model, and comparing its predictions against ground truth. You will be reusing the utilities you wrote for HW1 (or Piazza) for the data collection part (look for “get this from Piazza” markers).

What commands to run:

python cs285/scripts/run_hw4_mb.py --exp_name q1_cheetah_n500_arch1x32

--env_name cheetah-cs285-v0 --add_sl_noise --n_iter 1 -batch_size_initial 20000 --num_agent_train_steps_per_iter 500 -n_layers 1 --size 32 --scalar_log_freq -1 --video_log_freq -1 -mpc_action_sampling_strategy 'random'

python cs285/scripts/run_hw4_mb.py --exp_name q1_cheetah_n5_arch2x250

--env_name cheetah-cs285-v0 --add_sl_noise --n_iter 1 -batch_size_initial 20000 --num_agent_train_steps_per_iter 5 -n_layers 2 --size 250 --scalar_log_freq -1 --video_log_freq -1 -mpc_action_sampling_strategy 'random'

python cs285/scripts/run_hw4_mb.py --exp_name q1_cheetah_n500_arch2x250

--env_name cheetah-cs285-v0 --add_sl_noise --n_iter 1 -batch_size_initial 20000 --num_agent_train_steps_per_iter 500 -n_layers 2 --size 250 --scalar_log_freq -1 --video_log_freq -1 -mpc_action_sampling_strategy 'random'

Your code will produce plots inside your logdir that illustrate your model prediction error (MPE). The code will also produce a plot of the losses over time. For the first command, the loss should go below 0.2 by the iteration 500. These plots illustrate, for a fixed action sequence, the difference between your model’s predictions (red) and the ground-truth states (green). Each plot corresponds to a different state element, and the title reports the mean mean-squared-error across all state elements. As illustrated in the commands above, try different neural network architectures as well different amounts of training. Compare the results by looking at the loss values (i.e., itr 0 losses.png), the qualitative model predictions (i.e., itr 0 predictions.png), as well as the quantitative MPE values (i.e., in the title of itr 0 predictions.png).

Problem 2

What will you implement:

Action selection using your learned dynamics model and a given reward function.

n) What commands to run:

python cs285/scripts/run_hw4_mb.py --exp_name q2_obstacles_singleiteration --env_name obstacles-cs285-v0 -add_sl_noise --num_agent_train_steps_per_iter 20 --n_iter 1 -batch_size_initial 5000 --batch_size 1000 --mpc_horizon 10 -mpc_action_sampling_strategy 'random'

Recall the overall flow of our rl trainer.py. We first collect data with our policy (which starts as random), we then train our model on that collected data, and we then evaluate the resulting MPC policy (which now uses the trained model). To verify that your MPC is indeed doing reasonable action selection, run the command above and compare Train AverageReturn (which was the execution of random actions) to Eval AverageReturn (which was the execution of MPC using a model that was trained on the randomly collected training data). You can expect Train AverageReturn to be around -160 and Eval AverageReturn to be around -70 to -50.

Problem 3

What will you implement:

MBRL algorithm with on-policy data collection and iterative model training..

What commands to run:

python cs285/scripts/run_hw4_mb.py --exp_name q3_obstacles --env_name obstacles-cs285-v0 --add_sl_noise --num_agent_train_steps_per_iter 20 --batch_size_initial 5000 --batch_size 1000 --mpc_horizon 10 -n_iter 12 --mpc_action_sampling_strategy 'random'

python cs285/scripts/run_hw4_mb.py --exp_name q3_reacher --env_name reacher-cs285-v0 --add_sl_noise --mpc_horizon 10 -num_agent_train_steps_per_iter 1000 --batch_size_initial 5000 -batch_size 5000 --n_iter 15 --mpc_action_sampling_strategy 'random'

python cs285/scripts/run_hw4_mb.py --exp_name q3_cheetah --env_name cheetah-cs285-v0 --mpc_horizon 15 --add_sl_noise -num_agent_train_steps_per_iter 1500 --batch_size_initial 5000 -batch_size 5000 --n_iter 20 --mpc_action_sampling_strategy 'random'

You should expect rewards of around -25 to -20 for the obstacles env (takes 40 minutes), rewards of around -250 to -300 for the reacher env (takes 2-3 hours), and rewards of around 250-350 for the cheetah env takes 3-4 hours. All numbers assume no GPU.

Problem 4

What will you implement:

You will compare the performance of your MBRL algorithm as a function of three hyperparameters: the number of models in your ensemble, the number of random action sequences considered during each action selection, and the MPC planning horizon.

What code files to fill in: None.

What commands to run:

python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_horizon5 -env_name reacher-cs285-v0 --add_sl_noise --mpc_horizon 5 -mpc_action_sampling_strategy 'random' -num_agent_train_steps_per_iter 1000 --batch_size 800 --n_iter 15 -mpc_action_sampling_strategy 'random'

python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_horizon15 -env_name reacher-cs285-v0 --add_sl_noise --mpc_horizon 15 -num_agent_train_steps_per_iter 1000 --batch_size 800 --n_iter 15 -mpc_action_sampling_strategy 'random'

python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_horizon30 -env_name reacher-cs285-v0 --add_sl_noise --mpc_horizon 30 -num_agent_train_steps_per_iter 1000 --batch_size 800 --n_iter 15 -mpc_action_sampling_strategy 'random'

python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_numseq100 -env_name reacher-cs285-v0 --add_sl_noise --mpc_horizon 10 -num_agent_train_steps_per_iter 1000 --batch_size 800 --n_iter 15 -mpc_num_action_sequences 100 --mpc_action_sampling_strategy 'random

' python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_numseq1000 -env_name reacher-cs285-v0 --add_sl_noise --mpc_horizon 10 -num_agent_train_steps_per_iter 1000 --batch_size 800 --n_iter 15 -mpc_num_action_sequences 1000 --mpc_action_sampling_strategy ' random'

python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_ensemble1 -env_name reacher-cs285-v0 --ensemble_size 1 --add_sl_noise -mpc_horizon 10 --num_agent_train_steps_per_iter 1000 --batch_size

800 --n_iter 15 --mpc_action_sampling_strategy 'random' python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_ensemble3 -env_name reacher-cs285-v0 --ensemble_size 3 --add_sl_noise -mpc_horizon 10 --num_agent_train_steps_per_iter 1000 --batch_size

800 --n_iter 15 --mpc_action_sampling_strategy 'random' python cs285/scripts/run_hw4_mb.py --exp_name q4_reacher_ensemble5 -env_name reacher-cs285-v0 --ensemble_size 5 --add_sl_noise -mpc_horizon 10 --num_agent_train_steps_per_iter 1000 --batch_size

800 --n_iter 15 --mpc_action_sampling_strategy 'random'

Problem 5

What will you implement:

You will compare the performance of your MBRL algorithm with action selecting performed by random-shooting (what you have done up to this point) and CEM.

Because CEM can be much slower than random-shooting, we will only run MBRL for 5 iterations for this problem. We will try two hyperparameter settings for CEM and compare their performance to random-shooting.