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Register a new userContrastive Reinforcement Learning of Symbolic Reasoning Domains
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Added by
Gabriel Poesia
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Abstract symbolic reasoning, as required in domains such as mathematics and logic, is a key component of human intelligence. Solvers for these domains have important applications, especially to computer-assisted education. But learning to solve symbolic problems is challenging for machine learning algorithms. Existing models either learn from human solutions or use hand-engineered features, making them expensive to apply in new domains. In this paper, we instead consider symbolic domains as simple environments where states and actions are given as unstructured text, and binary rewards indicate whether a problem is solved. This flexible setup makes it easy to specify new domains, but search and planning become challenging. We introduce four environments inspired by the Mathematics Common Core Curriculum, and observe that existing Reinforcement Learning baselines perform poorly. We then present a novel learning algorithm, Contrastive Policy Learning (ConPoLe) that explicitly optimizes the InfoNCE loss, which lower bounds the mutual information between the current state and next states that continue on a path to the solution. ConPoLe successfully solves all four domains. Moreover, problem representations learned by ConPoLe enable accurate prediction of the categories of problems in a real mathematics curriculum. Our results suggest new directions for reinforcement learning in symbolic domains, as well as applications to mathematics education.
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Symbolic planning models allow decision-making agents to sequence actions in arbitrary ways to achieve a variety of goals in dynamic domains. However, they are typically handcrafted and tend to require precise formulations that are not robust to human error. Reinforcement learning (RL) approaches do not require such models, and instead learn domain dynamics by exploring the environment and collecting rewards. However, RL approaches tend to require millions of episodes of experience and often learn policies that are not easily transferable to other tasks. In this paper, we address one aspect of the open problem of integrating these approaches: how can decision-making agents resolve discrepancies in their symbolic planning models while attempting to accomplish goals? We propose an integrated framework named SPOTTER that uses RL to augment and support (spot) a planning agent by discovering new operators needed by the agent to accomplish goals that are initially unreachable for the agent. SPOTTER outperforms pure-RL approaches while also discovering transferable symbolic knowledge and does not require supervision, successful plan traces or any a priori knowledge about the missing planning operator.
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Symbolic control techniques aim to satisfy complex logic specifications. A critical step in these techniques is the construction of a symbolic (discrete) abstraction, a finite-state system whose behaviour mimics that of a given continuous-state system. The methods used to compute symbolic abstractions, however, require knowledge of an accurate closed-form model. To generalize them to systems with unknown dynamics, we present a new data-driven approach that does not require closed-form dynamics, instead relying only the ability to evaluate successors of each state under given inputs. To provide guarantees for the learned abstraction, we use the Probably Approximately Correct (PAC) statistical framework. We first introduce a PAC-style behavioural relationship and an appropriate refinement procedure. We then show how the symbolic abstraction can be constructed to satisfy this new behavioural relationship. Moreover, we provide PAC bounds that dictate the number of data required to guarantee a prescribed level of accuracy and confidence. Finally, we present an illustrative example.
We address one-shot imitation learning, where the goal is to execute a previously unseen task based on a single demonstration. While there has been exciting progress in this direction, most of the approaches still require a few hundred tasks for meta-training, which limits the scalability of the approaches. Our main contribution is to formulate one-shot imitation learning as a symbolic planning problem along with the symbol grounding problem. This formulation disentangles the policy execution from the inter-task generalization and leads to better data efficiency. The key technical challenge is that the symbol grounding is prone to error with limited training data and leads to subsequent symbolic planning failures. We address this challenge by proposing a continuous relaxation of the discrete symbolic planner that directly plans on the probabilistic outputs of the symbol grounding model. Our continuous relaxation of the planner can still leverage the information contained in the probabilistic symbol grounding and significantly improve over the baseline planner for the one-shot imitation learning tasks without using large training data.
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