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Reinforcement learning (RL) is a widely known technique to enable autonomous learning. Even though RL methods achieved successes in increasingly large and complex problems, scaling solutions remains a challenge. One way to simplify (and consequently accelerate) learning is to exploit regularities in a domain, which allows generalization and reduction of the learning space. While object-oriented Markov decision processes (OO-MDPs) provide such generalization opportunities, we argue that the learning process may be further simplified by dividing the workload of tasks amongst multiple agents, solving problems as multiagent systems (MAS). In this paper, we propose a novel combination of OO-MDP and MAS, called multiagent OO-MDP (MOO-MDP). Our proposal accrues the benefits of both OO-MDP and MAS, better addressing scalability issues. We formalize the general model MOO-MDP and present an algorithm to solve deterministic cooperative MOO-MDPs. We show that our algorithm learns optimal policies while reducing the learning space by exploiting state abstractions. We experimentally compare our results with earlier approaches in three domains and evaluate the advantages of our approach in sample efficiency and memory requirements.

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Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem include neural-guided search (e.g. using reinforcement learning) and genetic programming. In this work, we introduce a hybrid neural-guided/genetic programming approach to symbolic regression and other combinatorial optimization problems. We propose a neural-guided component used to seed the starting population of a random restart genetic programming component, gradually learning better starting populations. On a number of common benchmark tasks to recover underlying expressions from a dataset, our method recovers 65% more expressions than a recently published top-performing model using the same experimental setup. We demonstrate that running many genetic programming generations without interdependence on the neural-guided component performs better for symbolic regression than alternative formulations where the two are more strongly coupled. Finally, we introduce a new set of 22 symbolic regression benchmark problems with increased difficulty over existing benchmarks. Source code is provided at www.github.com/brendenpetersen/deep-symbolic-optimization.

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