Introduction to Reinforcement Learning for Molecular Design

Intro to deep reinforcement learning
and applications to molecular design
Dan Elton
UMD College Park Fuge group tea talk
delton@umd.edu
December 5, 2018
Dan Elton (UMD) Intro to RL for molecule design December 5, 2018 1 / 22

Overview
1 Intro to RL
The Bellman equation
TD learning
Value vs policy learning
2 Deep Q learning
3 RL for molecular optimization
Implementation details
Tricks
Results
Interpretation of Q-functions
Hillclimb-MLE
4 References

Basic concepts in RL
The goal of the RL agent is to maximized the expected return, which is
the sum of future rewards:
Gt =
k=1,···
rt+k
Normally we want to include a discount factor 0 ≥ γ ≤ 1:
Gt =
k=1,···
γk−1
rt+k

Basic concepts in RL, continued...
A policy π = {(si , ai )} is a collection of all the possible (state, action)
pairs, that speciﬁes completely the behavior of the agent.
A state-value function V π(s) under policy π is the expected future
return obtained by starting in state s and following policy π.
An action-value function Qπ(s, a) under policy π is the total future
return expected by starting in state s, taking action a and following policy
π from there.
An action-value function can may be related to a policy via a softmax:
π(s, ai ) =
eβQ(s,ai )
j
eβQ(s,aj )
When β = ∞ this results in a “greedy” policy that always exploits the highest value
action. A lower β is a more “explorative” policy. Another option is to use an ε-greedy
policy.

The Bellman equation
V π
(s) = E[Gt|St = s]
= E[rt+1 + γGt+1|St = s]
=
a
π(a|s)
s ,r
p(s , r|s, a)[r + γE(Gt+1|St+1|St+1 = s ])
V π
(s) =
a
π(a|s)
s r
p(s , r|s, a)[r + γV π
(s )] (1)
If we know p(s , r|s, a), then we can calculate V π(s) for all s, which may
be denoted as a vector Vπ. The Bellman equation must be solved
recursively, but it can be proven the recursive solution method converges
correctly. However normally we do not know p(s , r|s, a) in advance. In
that case, we can use some form of value function learning like
TD-learning. With value function based method we need to learn a good
policy. Thus we need to start from a random (equiprobable action) policy,
run it forward, and perform policy evaluation and policy iteration.

Other jargon
A model free method does not require a model for the transition dynamics
p(s , r|s, a) to be learned. Instead , it learns through episodes / samples.
An oﬀ policy method learns the optimal greedy policy while following a
diﬀerent policy that ensures exploration (such as ε-greedy).

Temporal diﬀerence (TD) learning
A simple method for value function learning is TD-learning. The
algorithm is as follows:
Initialize V (s) arbitrarily for all states s. Choose a policy π(s, a) to
evaluate. Pick a random starting state s
Repeat for each time step t:
1. Pick an action a in state s, according to the policy π(s, a).
2. Act with a and move from state s to state s , collect reward r,
compute the TD-error: δ = r + γV (s ) − V (s).
3. Update V (s) according to : V (s) ← V (s) + αδ
4. Move to next state s ← s .
TD-learning has the following properties:
It is an online method, also called a “bootstrap” method.
It can be proven that the method converges to the exact V π(s) for a
given policy.

Value function learning vs policy gradient methods
Broadly speaking, RL methods can be broken into two categories:
Value function learning
Learn value function or action value function. UseBellman equation or
TD-learning type approach. Techniques include Q learning and
actor-critic methods.
When it works, it can be much more sample efficient. Empirically
these methods converge faster, although there is so far no
mathematical proof they always converge faster.
Policy learning & policy gradient methods
The canonical policy gradient method is the REINFORCE algorithm,
which is used in the ORGAN for molecule generation and several
papers on molecular generation with RNNs
usuall requires doing Monte-Carlo and running simulations to the final
end state (a complete ”episode”), which can be computationally
demanding or impossible in the case of continuous learning.
May suffer from high variance when estimating gradient.

Value function learning vs policy gradient methods,
continued..
Olivecrona et al. train an RNN with MLE and then fine-tune it using RL.
They argue for policy based learning as follows:
“For the problem addressed in this study, we believe that policy based
methods is the natural choice for three reasons:
Policy based methods can learn explicitly an optimal stochastic policy,
which is our goal.
The method used starts with a prior sequence model. The goal is to
finne tune this model according to some specifed scoring function.
Since the prior model already constitutes a policy, learning a finetuned
policy might require only small changes to the prior model.
The episodes in this case are short and fast to sample, reducing the
impact of the variance in the estimate of the gradients.”

Deep Q learning
Goal is to learn the action-value function Q(s, a), using a neural network
approximator with parameters θ, Q(s, a; θ). Goal is to approximate the
optimal action-value function Q∗(s, a):
Q∗,π
(s, a) = maxπE[Gt|St = s, At = a, π]
The general Bellman equation for Qπ(s, a) is
Qπ
(s, a) =
s ,r
p(s |s, a) r + γ
a
π(s , a )Qπ
(s , a )
The Bellman equation for Q∗,π is
Q∗,π
(s, a) =
s ,r
p(s |s, a) r + γmaxa Q∗,π
(s , a )|s, a
This can be solved iteratively as
Qπ
i+1(s, a) =
s ,r
p(s |s, a) r + γmaxa Qπ
i (s , a )|s, a (2)

Deep Q learning, continued..
In deep Q learning, the neural network model of Qπ(s, a) is retrained at the start of each
iteration of the Bellman equation solution to reduce the mean squared error between the LHS
and the RHS of the Bellman equation.
This approach was popularized by the DeepMind work :
Mnih, et al. “Human-level control through deep reinforcement learning”. Nature 518, pgs 529-533, 2015
A single deep Q-network based agent achieved human level performance on 49 Atari 2600
games, receiving only pixel values and game score as inputs.
input was 210x160 color video at 60 Hz

Experience replay
Improves stability and eﬃciency of deep Q learning. The experience of
the agent at each timestep et = (st, at, rt, st+1) are stored into a dataset
Dt = {e1, · · · et} which is assembled over many eipsodes (runs).
Then, each time Q is retrained, minibatch learning is performed using not
only the current state but also a set of experiences drawn randomly from
D.

Deep Q Learning for Molecular Optimization
Zhou, et al. “Optimization of Molecules Via Deep Reinforcement Learning”. Oct. 2018,
arXiv:1810.08678v2.
We have a Markov decision process MDP(S, A, {Psa}, R)
S is the state space. s ∈ S is a tuple, (m, t) where m is the molecule and t is the
number of steps taken. The number of steps that can be taken is limited to T,
leading to a ﬁnite (but still very large) state space.
A is the action space. Possible actions are:
Atom addition - this is a replacement of implicit hydrogen(s) with some other atom
(ensuring valence rules are followed).
Bond addition - this can be performed with atoms with ”free valence” (which
doesn’t include implicit hydrogens).
Bond removal - this is either reducing the order of a bond (ie from double to
single), or removing a bond altogether. If removal of a bond results in a
disconnected atom, that atom is removed as well.
{Psa} are the state transition probabilities. They is set to 1 here, meaning state
transitions are deterministic.
R denotes the reward funcction of the state (m, t). Rewards are calculated at each
step. However, to ensure that that the ﬁnal state is rewarded more than
intermediary states, a discount factor of γT−t
is applied. They used γ = 0.99

Implementation details
Molecules are converted to a vector using a Morgan ﬁngerprint with radius
3 and length 2048. They used a 4-layer neural net with ReLu activation
and layer sizes of [1024,512,128,32]
They used ε-greedy policy exploration with linear annealing of ε from 1 to
0.001.
They used multiple objective RL. This involves a vector of rewards
rt = [r1,t, · · · , rk,t]. Instead of just doing a linear weighted sum to get a
new scalar reward, Zhou et al. learn separate Qi (s, a) for the expected
return from each reward. Zhou et al. implement a multitask neural
network with separate outputs for each Qi (s, a). Optimal action is chosen
via a scalarized Q:
at = max
a
wT
Q(s, a) (3)
where w ∈ Rk is a vector of weights. This method can have issues if there
are competition between rewards can yield sub-optimal results.
A review of multiple objective RL methods can be found in Liu, et al. IEEE
Transactions on Systems, Man, and Cybernetics 2015, 45, 385-398.

Tricks
We talked about using a softmax or ε-greedy learning to allow for
exploration.
following:
Osband et al. “Deep Exploration via Randomized Value Functions”.
arXiv:1703.07608 (2017)
They train H independent Q functions each trained on a diﬀerent subset
of samples.
Other tricks they used:
prioritized experience replay
Double Q-learning

Results

Results
Beneﬁts of the “DQN” approach
Starts from scratch
No need to train a generative model. (which can take signiﬁcant GPU time
(weeks))
Possible weaknesses of the “DQN” approach
Starts from scratch (Olivecrona et al. talk about “drift” being an issue with RL)
Needs carefully tuned reward function

Reward curve

Interpretation of Q-functions

Hillclimb-MLE
Neil et al. (2018) introduce “Hillclimb-MLE” for optimization with a MLE-trained RNN:

References
Luca Mazzucato (2011)
Computational neuroscience: a physicist’s point of view
Richard S. Sutton and Andrew G. Barto (2018)
Reinforcement Learning: An Introduction, 2nd edition
Mnih, et al. (2015)
Human-level control through deep reinforcement learning
Nature 518, pgs 529-533
Zhou, Kearnes, Li, Zare, Riley (2018)
Optimization of Molecules via Deep Reinforcement Learning
arXiv:1810.08678v2
Olivecrona et al. (2017)
Molecular de-novo design through deep reinforce-ment learning
Journal of Cheminformatics, 9 (1)

The End

Introduction to Reinforcement Learning for Molecular Design

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