Reinforcement learning-based methods for constructing solutions to combinatorial optimization problems are rapidly approaching the performance of humandesigned algorithms. To further narrow the gap, learning-based approaches must efficiently explore the solution space during the search process. Recent approaches artificially increase exploration by enforcing diverse solution generation through handcrafted rules, however, these rules can impair solution quality and are difficult to design for more complex problems. In this paper, we introduce PolyNet, an approach for improving exploration of the solution space by learning complementary solution strategies. In contrast to other works, PolyNet uses only a single-decoder and a training schema that does not enforce diverse solution generation through handcrafted rules. We evaluate PolyNet on four combinatorial optimization problems and observe that the implicit diversity mechanism allows PolyNet to find better solutions than approaches the explicitly enforce diverse solution generation. There have been remarkable advancements in recent years in the field of learning-based approaches for solving combinatorial optimization (CO) problems (Bello et al., 2016; Kool et al., 2019; Kwon et al., 2020). Notably, reinforcement learning (RL) methods have emerged that build a solution to a problem step-by-step in a sequential decision making process. Initially, these construction techniques struggled to produce high-quality solutions. However, recent methods have surpassed even established operations research heuristics, such as LKH3, for simpler, smaller-scale routing problems. Learning-based approaches thus now have the potential to become versatile tools, capable of learning specialized heuristics tailored to unique business-specific problems. Moreover, with access to sufficiently large training datasets, they may consistently outperform off-the-shelf solvers in numerous scenarios. This work aims to tackle some of the remaining challenges that currently impede the widespread adoption of learning-based heuristic methods in practical applications.

Margaret Trautner Department of Mathematics Sai Ravela † Department of Earth, Atmospheric, and Planetary Sciences Earth Signals and Systems Group, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (Dated: November 26, 2019) Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Modeled as recurrent networks embedding a continuous neural differential equation, they achieve fully neural temporal output. Using the polynomial class of dynamical systems, we demonstrate equivalence of neural and numerical integration. I. INTRODUCTION Neural dynamical systems are dynamical systems described at least in part by neural networks. Our interest in the subject emerges in the context of Systems Dynamics and Optimization [21] (SDO), which is central to many applications such as storm prediction [19], climate-risk based decision support [22], or autonomous observatories [25]. The SDO cycle conceptually involves a forward path dynamically parameterizing, reducing, calibrating, initializing and simulating numerical models, and quantifying their uncertainties. SDO further involves a return path for adaptive observation, inversion and estimation.