  Consider mutli-goal tasks that involve static environments and dynamic goals.
Examples of such tasks, such as goal-directed navigation and pick-and-place in
robotics, abound. Two types of Reinforcement Learning (RL) algorithms are used
for such tasks: model-free or model-based. Each of these approaches has
limitations. Model-free RL struggles to transfer learned information when the
goal location changes, but achieves high asymptotic accuracy in single goal
tasks. Model-based RL can transfer learned information to new goal locations by
retaining the explicitly learned state-dynamics, but is limited by the fact
that small errors in modelling these dynamics accumulate over long-term
planning. In this work, we improve upon the limitations of model-free RL in
multi-goal domains. We do this by adapting the Floyd-Warshall algorithm for RL
and call the adaptation Floyd-Warshall RL (FWRL). The proposed algorithm learns
a goal-conditioned action-value function by constraining the value of the
optimal path between any two states to be greater than or equal to the value of
paths via intermediary states. Experimentally, we show that FWRL is more
sample-efficient and learns higher reward strategies in multi-goal tasks as
compared to Q-learning, model-based RL and other relevant baselines in a
tabular domain.
