C2 294 HW4: Modl-Based RL solved

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1 Introduction
The goal of this assignment is to get experience with model-learning in the context of RL,
and to use simple model-based methods (particularly, Model Predictive Control (MPC)) for
controlling agents. The experiments you will run are based on (Nagabandi, 2017)1
.
2 Algorithm and Implementation
2.1 Algorithm
The algorithm you will implement is described in Algorithm 1. The exact rule for the MPC
action-selection is described in Algorithm 2.
2.2 Code Setup
The following files are ones you are expected to modify:
• main.py
– Contains the main loop which calls the rollout sampler, fits the dynamics model,
and aggregates data.
– You will implement the entire main loop. (Some structure is provided to guide
you.)
1“Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free FineTuning”, Anusha Nagabandi, Gregory Kahn, Ronald S. Fearing, Sergey Levine. https://arxiv.org/
abs/1708.02596
1
Algorithm 1 Model-Based Control with On-Policy Data Aggregation
Sample a random set of Nrand trajectories Drand from environment E
Initialize dataset D to Drand
for k = 0, 1, 2, … do
• Fit dynamics model fθ according to
θk = arg min
θ
1
N
X
(s,a,s0)∈D
kfθ(s, a) − s
0
k
2
2
using the Adam optimization algorithm, starting from initial parameters θk−1 (or
if k = 0, starting from random initial parameter values).
• Sample a set of Nrl on-policy trajectories Drl from E using an policy which selects
actions according to Algorithm 2.
• Aggregate data: D = D ∪ Drl.
end for
Algorithm 2 MPC Action Selection Using Dynamics Model fθ
input Initial state s, number of simulated rollouts K, path length (horizon) for simulated
rollouts H, cost function on trajectories C, dynamics model fθ.
• Sample K sequences of Hmpc actions, {a
j
1
, · · · , a
j
H}j=1,…,K
• Use dynamics model fθ to generate associated simulated rollouts:
s
j
t+1 = fθ(s
j
t
, a
j
t
),
where for all j, s
j
0 = s.
• Use C to evaluate fictitious trajectories τ
j = (s
j
0
, a
j
0
, …, s
j
H, a
j
H, s
j
H+1). Find the best
trajectory, j
∗ = arg minj C(τ
j
).
• Return a
j

0
.
• dynamics.py
– Contains the dynamics model code.
– The dynamics model object has two key methods: fit, which runs an iteration
of the optimization algorithm, and predict, which performs inference using the
learned model.
– You will implement both of these.
• controllers.py
– Contains the MPC controller code.
– To produce an action for a given state, the MPC controller uses the learned
dynamics model to generate imaginary rollouts using random actions, uses a cost
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function to determine the best imaginary rollout, and selects the first action of
the best imaginary rollout.
– You will implement the action-selection process.
The file cost_functions.py contains functions you will use to evaluate the imaginary
rollouts generated with your learned dynamics model.
The file cheetah_env.py contains the environment (a half-cheetah robot) you will be
testing your code with.
The files logz.py and plots.py are utility files which you have used before (in homework
2), and you will not modify them.
After you fill in the blanks, you should be able to just run python main.py with some
command line options to perform the experiments. To visualize the results, you can run
python plot.py path/to/logdir. (Full documentation for the plotter can be found
in plot.py.)
2.3 Implementation Details
• When implementing compute_normalization in main.py:
– Make sure to produce vector-valued means and stds for the various quantities.
– That is, you should have means and stds for each component of each of those
vectors.
• Use the AdamOptimizer to train the dynamics model. For details on how many steps
of gradient descent to take, we recommend that you study the experimental details in
(Nagabandi, 2017).
• When implementing the dynamics model:
– Pay careful attention to the keyword args for the dynamics model. The normalization vectors are inputs here, and you need these for normalizing inputs and
denormalizing outputs from the model.
– You want the neural network for your dynamics model to output differences in
states, instead of outputting next states directly. Then using the estimated state
difference ∆ and the current state ˆ s, you will predict the estimated next state ˆs
0
according to:

0 = s + ∆ˆ .
– How to use the normalization statistics: given a state s and an action a, and
normalization statistics µs, σs, µa, σa, µ∆, σ∆ (where ∆ = s
0 − s), you want your
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network to compute an estimate of the state difference ∆ according to ˆ
∆ = ˆ µ∆ + σ∆ fθ

s − µs
σs + 
,
a − µa
σa + 

,
where is an elementwise vector multiply and  is a small positive value (to
prevent divide-by-zero).
• When implementing the MPC controller:
– To evaluate the costs of imaginary rollouts, use trajectory_cost_fn, which
requires a per-timestep cost_fn as an argument. Notice that the MPC controller
gets a cost function as a keyword argument—this is what you should use!
– When generating the imaginary rollouts starting from a state s, be efficient and
batch the computation. At the first step, broadcast s to have shape (number of
fictional rollouts, observation dim), and then use that as an input to the dynamics
model prediction to produce the batch of next steps.
– The cost functions are also designed for batch computations, so you can feed the
whole batch of trajectories at once to trajectory_cost_fn. For details on
how, read the code.
3 Experiments
• Fit a dynamics model to random data alone and use the learned dynamics model in your
MPC controller to control the cheetah robot. Report your performance (copy/paste
the log output into your report).
• Run the full algorithm, including on-policy data aggregation, for 15 iterations. Make
a graph of the performance (average return) at each iteration. How does performance
change when the on-policy data is included?
4 Bonus
Choose any (or all) of the following:
• Use this method to get another robot to move forward – could be the swimmer, the
ant or anything else.
• Implement a better way of choosing actions during MPC than random sampling, and
show the difference in performance with this method.
• Any other algorithmic improvements to the dynamics model or the controller to improve sample complexity or performance.
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5 Submission
Your report should be a one or two page document containing the results for your experiments
from section 4 and all command line expressions you used to run your experiments.
Also provide a zip file including all of the files in your code, along with any special instructions
needed to exactly duplicate your results.
Turn this in by October 18th 11:59pm by emailing your report and code to
berkeleydeeprlcourse@gmail.com, with subject line “Deep RL Assignment 4”.
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