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# HW4: Model-Based RL

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CS285 Deep Reinforcement Learning HW4:
Model-Based RL
1 Introduction
The goal of this assignment is to get experience with model-based reinforcement
learning. 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)
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
(st,at,st+1)∈D
k(st+1 − st) − fθ(st, at)k
2
2
(3)
=
X
(st,at,st+1)∈D
k∆t+1 − ∆ˆ
t+1k
2
2
(4)
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
(st,at,st+1)∈D
kNormalize(st+1 − st) − fθ(st, at)k
2
2
. (5)
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 = arg min
at:∞
X∞
t
0=t
c(ˆst
0 , at
0 ) where ˆst
0+1 = ˆst
0 + fθ(ˆst
0 , at
0 ). (7)
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.
A∗ = arg min
{A(0),…,A(K−1)}
t+
X
H−1
t
0=t
c(ˆst
0 , at
0 ) s.t. ˆst
0+1 = ˆst
0 + fθ(ˆst
0 , at
0 ), (8)
2
in which A(k) = (a
(k)
t
, . . . , a
(k)
t+H−1
) 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
A better alternative to this random-shooting optimization approach is the crossentropy 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 randomshooting. 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:
3
Algorithm 1 Model-Based RL with On-Policy Data
Run base policy π0(at, st) (e.g., random policy) to collect D = {(st, at, st+1)}
while not done do
Train fθ using D (Eqn. 4)
st ← current agent state
for rollout number m = 0 to M do
for timestep t = 0 to T do
A∗ = πMPC(at, st) where πMPC is obtained from random-shooting or
CEM
at ← first action in A∗
Execute at and proceed to next state st+1
Add (st, at, st+1) to D
end
end
end
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 {fθn
}
N
n=1, and average
their predictions to get your final predictions
f(st, at) = 1
N
X
N
n=1
fθn
(st, at). (9)
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.
4
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 code files to fill in:
1. cs285/agents/mb_agent.py
2. cs285/models/ff_model.py
3. cs285/infrastructure/utils.py
4. cs285/policies/MPC_policy.py (just one line labeled TODO(Q1)
for now)
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).
5
What to submit: For this question, submit the qualitative model predictions
(itr 0 predictions.png) for each of the three runs above. Comment on which
model performs the best and why you think this might be the case.
Note that for these qualitative model prediction plots, we intend for you to just
copy the png images produced by the code.
6
Problem 2
What will you implement:
Action selection using your learned dynamics model and a given reward function.
What code files to fill in:
1. cs285/policies/MPC_policy.py (all lines labeled TODO(Q2), i.e.
everything except the CEM section)
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
be around -70 to -50.
What to submit:
Submit this run as part of your run logs, and include a plot of Train AverageReturn
and Eval AverageReturn in your pdf. Note that these will just be single dots
on the plot, since we ran this for just 1 iteration.
7
Problem 3
What will you implement:
MBRL algorithm with on-policy data collection and iterative model training.
What code files to fill in:
None. You should already have done everything that you need, because rl trainer.py
already aggregates your collected data into a replay buffer. Thus, iterative training means to just train on our growing replay buffer while collecting new data
at each iteration using the most newly trained model.
What commands to run:
python cs285/scripts/run_hw4_mb.py –exp_name q3_obstacles –env_name
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
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
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.
What to submit:
Submit these runs as part of your run logs, and include the performance plots
8
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’
What to submit:
1) Submit these runs as part of your run logs.
9
2) Include the following plots (as well as captions that describe your observed
trends) of the following:
• effect of ensemble size
• effect of the number of candidate action sequences
• efffect of planning horizon
Be sure to include titles and legends on all of your plots, and be sure to generate your plots by extracting the corresponding performance numbers from your
saved tensorboard eventfiles.
10
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.
What code files to fill in:
1. cs285/policies/MPC_policy.py
What commands to run:
python cs285/scripts/run_hw4_mb.py –exp_name q5_cheetah_random —
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 5 –mpc_action_sampling_strategy ‘random’
python cs285/scripts/run_hw4_mb.py –exp_name q5_cheetah_cem_2 —
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 5 –mpc_action_sampling_strategy ‘cem’
–cem_iterations 2
python cs285/scripts/run_hw4_mb.py –exp_name q5_cheetah_cem_4 —
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 5 –mpc_action_sampling_strategy ‘cem’
–cem_iterations 4
You should expect rewards of 800 or higher when using CEM on the cheetah
env. The final CEM run takes 2-3 hours on GPU, and over twice as long without
GPU, so we recommend getting started early and using a GPU (e.g.
on Colab) for this problem!
What to submit:
1) Submit these runs as part of your run logs.
2) Include a plot comparing random-shooting with CEM, as well as captions
that describe how CEM affects results for different numbers of sampling iterations (2 vs. 4).
Be sure to include a title and legend on your plot, and be sure to generate your
plot by extracting the corresponding performance numbers from your saved tensorboard eventfiles.
11
Submission
3.2 Submitting the PDF
Your report should be a PDF document containing the plots and responses
indicated in the questions above.
3.3 Submitting the Code and Logs
In order to turn in your code and experiment logs, create a folder that contains
the following:
• A folder named data with all the experiment runs from this assignment.
Do not change the names originally assigned to the folders, as
specified by exp name in the instructions. To minimize submissions size, please include runs with video logging disabled. If you would
like to reuse your video logging runs, please see the script provided in
cs285/scripts/filter_events.py.
• The cs285 folder with all the .py files, with the same names and directory structure as the original homework repository (not include the
data/ folder). A plotting script should also be submitted, which should
be a python script (or jupyter notebook) such that running it can generate all plots from your pdf. This plotting script should extract its values
directly from the experiments in your run logs and should not have
hardcoded reward values.
As an example, the unzipped version of your submission should result in the
following file structure. Make sure that the submit.zip file is below 15MB
and that they include the prefix hw4 mb .
12
submit.zip
data
hw4 q1 …
events.out.tfevents.1567529456.e3a096ac8ff4

cs285
agents
mb agent.py

policies HW4: Model-Based RL