A Reinforcement Learning Environment for Mathematical Reasoning via Program SynthesisJoseph Palermo, Johnny Ye, Alok Singh
We convert the DeepMind Mathematics Dataset into a reinforcement learning environment by interpreting it as a program synthesis problem. Each action taken in the environment adds an operator or an input into a discrete compute graph. Graphs which compute correct answers yield positive reward, enabling the optimization of a policy to construct compute graphs conditioned on problem statements. Baseline models are trained using Double DQN on various subsets of problem types, demonstrating the capability to learn to correctly construct graphs despite the challenges of combinatorial explosion and noisy rewards.
Detecting Spiky Corruption in Markov Decision ProcessesJason Mancuso, Tomasz Kisielewski, David Lindner et al.
Current reinforcement learning methods fail if the reward function is imperfect, i.e. if the agent observes reward different from what it actually receives. We study this problem within the formalism of Corrupt Reward Markov Decision Processes (CRMDPs). We show that if the reward corruption in a CRMDP is sufficiently "spiky", the environment is solvable. We fully characterize the regret bound of a Spiky CRMDP, and introduce an algorithm that is able to detect its corrupt states. We show that this algorithm can be used to learn the optimal policy with any common reinforcement learning algorithm. Finally, we investigate our algorithm in a pair of simple gridworld environments, finding that our algorithm can detect the corrupt states and learn the optimal policy despite the corruption.