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)

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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.

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

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

sufficient for solving long-horizon tasks.

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:

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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.

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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).

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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.

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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

can expect Train AverageReturn to be around -160 and Eval AverageReturn to

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.

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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

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.

What to submit:

Submit these runs as part of your run logs, and include the performance plots

in your pdf.

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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.

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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.

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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.

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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 .

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submit.zip

data

hw4 q1 …

events.out.tfevents.1567529456.e3a096ac8ff4

…

cs285

agents

mb agent.py

…

policies

…

…

README.md

…

If you are a Mac user, do not use the default “Compress” option to create

the zip. It creates artifacts that the autograder does not like. You may use zip

-vr submit.zip submit -x “*.DS Store” from your terminal.

Turn in your assignment on Gradescope. Upload the zip file with your code and

log files to HW4 Code, and upload the PDF of your report to HW4.

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Sale!