  This work compares ways of extending Reinforcement Learning algorithms to
Partially Observed Markov Decision Processes (POMDPs) with options. One view of
options is as temporally extended action, which can be realized as a memory
that allows the agent to retain historical information beyond the policy's
context window. While option assignment could be handled using heuristics and
hand-crafted objectives, learning temporally consistent options and associated
sub-policies without explicit supervision is a challenge. Two algorithms, PPOEM
and SOAP, are proposed and studied in depth to address this problem. PPOEM
applies the forward-backward algorithm (for Hidden Markov Models) to optimize
the expected returns for an option-augmented policy. However, this learning
approach is unstable during on-policy rollouts. It is also unsuited for
learning causal policies without the knowledge of future trajectories, since
option assignments are optimized for offline sequences where the entire episode
is available. As an alternative approach, SOAP evaluates the policy gradient
for an optimal option assignment. It extends the concept of the generalized
advantage estimation (GAE) to propagate option advantages through time, which
is an analytical equivalent to performing temporal back-propagation of option
policy gradients. This option policy is only conditional on the history of the
agent, not future actions. Evaluated against competing baselines, SOAP
exhibited the most robust performance, correctly discovering options for POMDP
corridor environments, as well as on standard benchmarks including Atari and
MuJoCo, outperforming PPOEM, as well as LSTM and Option-Critic baselines. The
open-sourced code is available at https://github.com/shuishida/SoapRL.
