Reward Machines provide an automaton-inspired structure for specifying instructions, safety constraints, and other temporally extended reward-worthy behaviour. By exposing the underlying structure of a reward function, they enable the decomposition of an RL task, leading to impressive gains in sample efficiency. Although Reward Machines and similar formal specifications have a rich history of application towards sequential decision-making problems, prior frameworks have traditionally ignored ambiguity and uncertainty when interpreting the domain-specific vocabulary forming the building blocks of the reward function. Such uncertainty critically arises in many real-world settings due to factors like partial observability or noisy sensors. In this work, we explore the use of Reward Machines for Deep RL in noisy and uncertain environments. We characterize this problem as a POMDP and propose a suite of RL algorithms that exploit task structure under uncertain interpretation of the domain-specific vocabulary. Through theory and experiments, we expose pitfalls in naive approaches to this problem while simultaneously demonstrating how task structure can be successfully leveraged under noisy interpretations of the vocabulary.

In Mixed Integer Linear Programming (MIP), a (strong) backdoor is a ``small" subset of an instance's integer variables with the following property: in a branch-and-bound procedure, the instance can be solved to global optimality by branching only on the variables in the backdoor. Constructing datasets of pre-computed backdoors for widely used MIP benchmark sets or particular problem families can enable new questions around novel structural properties of a MIP, or explain why a problem that is hard in theory can be solved efficiently in practice. Existing algorithms for finding backdoors rely on sampling candidate variable subsets in various ways, an approach which has demonstrated the existence of backdoors for some instances from MIPLIB2003 and MIPLIB2010. However, these algorithms fall short of consistently succeeding at the task due to an imbalance between exploration and exploitation. We propose BaMCTS, a Monte Carlo Tree Search framework for finding backdoors to MIPs. Extensive algorithmic engineering, hybridization with traditional MIP concepts, and close integration with the CPLEX solver have enabled our method to outperform baselines on MIPLIB2017 instances, finding backdoors more frequently and more efficiently.

Supervised learning can improve the design of state-of-the-art solvers for combinatorial problems, but labelling large numbers of combinatorial instances is often impractical due to exponential worst-case complexity. Inspired by the recent success of contrastive pre-training for images, we conduct a scientific study of the effect of augmentation design on contrastive pre-training for the Boolean satisfiability problem. While typical graph contrastive pre-training uses label-agnostic augmentations, our key insight is that many combinatorial problems have well-studied invariances, which allow for the design of label-preserving augmentations. We find that label-preserving augmentations are critical for the success of contrastive pre-training. We show that our representations are able to achieve comparable test accuracy to fully-supervised learning while using only 1% of the labels. We also demonstrate that our representations are more transferable to larger problems from unseen domains. Our code is available at https://github.com/h4duan/contrastive-sat.

Text-based games present a unique class of sequential decision making problem in which agents interact with a partially observable, simulated environment via actions and observations conveyed through natural language. Such observations typically include instructions that, in a reinforcement learning (RL) setting, can directly or indirectly guide a player towards completing reward-worthy tasks. In this work, we study the ability of RL agents to follow such instructions. We conduct experiments that show that the performance of state-of-the-art text-based game agents is largely unaffected by the presence or absence of such instructions, and that these agents are typically unable to execute tasks to completion. To further study and address the task of instruction following, we equip RL agents with an internal structured representation of natural language instructions in the form of Linear Temporal Logic (LTL), a formal language that is increasingly used for temporally extended reward specification in RL. Our framework both supports and highlights the benefit of understanding the temporal semantics of instructions and in measuring progress towards achievement of such a temporally extended behaviour. Experiments with 500+ games in TextWorld demonstrate the superior performance of our approach.

Propositional model counting, or #SAT, is the problem of computing the number of satisfying assignments of a Boolean formula. Many problems from different application areas, including many discrete probabilistic inference problems, can be translated into model counting problems to be solved by #SAT solvers. Exact #SAT solvers, however, are often not scalable to industrial size instances. In this paper, we present Neuro#, an approach for learning branching heuristics to improve the performance of exact #SAT solvers on instances from a given family of problems. We experimentally show that our method reduces the step count on similarly distributed held-out instances and generalizes to much larger instances from the same problem family. It is able to achieve these results on a number of different problem families having very different structures. In addition to step count improvements, Neuro# can also achieve orders of magnitude wall-clock speedups over the vanilla solver on larger instances in some problem families, despite the runtime overhead of querying the model.

We address the problem of teaching a deep reinforcement learning (RL) agent to follow instructions in multi-task environments. Instructions are expressed in a well-known formal language {–} linear temporal logic (LTL) {–} and can specify a diversity of complex, temporally extended behaviours, including conditionals and alternative realizations. Our proposed learning approach exploits the compositional syntax and the semantics of LTL, enabling our RL agent to learn task-conditioned policies that generalize to new instructions, not observed during training. To reduce the overhead of learning LTL semantics, we introduce an environment-agnostic LTL pretraining scheme which improves sample-efficiency in downstream environments. Experiments on discrete and continuous domains target combinatorial task sets of up to $\sim10^{39}$ unique tasks and demonstrate the strength of our approach in learning to solve (unseen) tasks, given LTL instructions.