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.
While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirces view that deduction, induction, and abduction form an irreducible set of reasoning primitives, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these synthetic tasks in a way that they are devoid of mathematical knowledge to ensure that only the fundamental reasoning biases can be learned from these tasks. This defines a new pre-training methodology called LIME (Learning Inductive bias for Mathematical rEasoning). Models trained with LIME significantly outperform vanilla transformers on three very different large mathematical reasoning benchmarks. Unlike dominating the computation cost as traditional pre-training approaches, LIME requires only a small fraction of the computation cost of the typical downstream task.
We study a security threat to reinforcement learning where an attacker poisons the learning environment to force the agent into executing a target policy chosen by the attacker. As a victim, we consider RL agents whose objective is to find a policy that maximizes reward in infinite-horizon problem settings. The attacker can manipulate the rewards and the transition dynamics in the learning environment at training-time, and is interested in doing so in a stealthy manner. We propose an optimization framework for finding an optimal stealthy attack for different measures of attack cost. We provide lower/upper bounds on the attack cost, and instantiate our attacks in two settings: (i) an offline setting where the agent is doing planning in the poisoned environment, and (ii) an online setting where the agent is learning a policy with poisoned feedback. Our results show that the attacker can easily succeed in teaching any target policy to the victim under mild conditions and highlight a significant security threat to reinforcement learning agents in practice.
While current benchmark reinforcement learning (RL) tasks have been useful to drive progress in the field, they are in many ways poor substitutes for learning with real-world data. By testing increasingly complex RL algorithms on low-complexity simulation environments, we often end up with brittle RL policies that generalize poorly beyond the very specific domain. To combat this, we propose three new families of benchmark RL domains that contain some of the complexity of the natural world, while still supporting fast and extensive data acquisition. The proposed domains also permit a characterization of generalization through fair train/test separation, and easy comparison and replication of results. Through this work, we challenge the RL research community to develop more robust algorithms that meet high standards of evaluation.
Neural inductive program synthesis is a task generating instructions that can produce desired outputs from given inputs. In this paper, we focus on the generation of a chunk of assembly code that can be executed to match a state change inside the CPU and RAM. We develop a neural program synthesis algorithm, AutoAssemblet, learned via self-learning reinforcement learning that explores the large code space efficiently. Policy networks and value networks are learned to reduce the breadth and depth of the Monte Carlo Tree Search, resulting in better synthesis performance. We also propose an effective multi-entropy policy sampling technique to alleviate online update correlations. We apply AutoAssemblet to basic programming tasks and show significant higher success rates compared to several competing baselines.
Despite recent success of deep network-based Reinforcement Learning (RL), it remains elusive to achieve human-level efficiency in learning novel tasks. While previous efforts attempt to address this challenge using meta-learning strategies, they typically suffer from sampling inefficiency with on-policy RL algorithms or meta-overfitting with off-policy learning. In this work, we propose a novel meta-RL strategy to address those limitations. In particular, we decompose the meta-RL problem into three sub-tasks, task-exploration, task-inference and task-fulfillment, instantiated with two deep network agents and a task encoder. During meta-training, our method learns a task-conditioned actor network for task-fulfillment, an explorer network with a self-supervised reward shaping that encourages task-informative experiences in task-exploration, and a context-aware graph-based task encoder for task inference. We validate our approach with extensive experiments on several public benchmarks and the results show that our algorithm effectively performs exploration for task inference, improves sample efficiency during both training and testing, and mitigates the meta-overfitting problem.
Joseph Palermo
,Johnny Ye
,Alok Singh
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(2021)
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"A Reinforcement Learning Environment for Mathematical Reasoning via Program Synthesis"
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Joseph Palermo
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