text: In this paper, we propose TauRieL and target Traveling Salesman Problem (TSP) since it has broad applicability in theoretical and applied sciences. TauRieL utilizes an actor-critic inspired architecture that adopts ordinary feedforward nets to obtain a policy update vector @math . Then, we use @math to improve the state transition matrix from which we generate the policy. Also, the state transition matrix allows the solver to initialize from precomputed solutions such as nearest neighbors. In an online learning setting, TauRieL unifies the training and the search where it can generate near-optimal results in seconds. The input to the neural nets in the actor-critic architecture are raw 2-D inputs, and the design idea behind this decision is to keep neural nets relatively smaller than the architectures with wide embeddings with the tradeoff of omitting any distributed representations of the embeddings. Consequently, TauRieL generates TSP solutions two orders of magnitude faster per TSP instance as compared to state-of-the-art offline techniques with a performance impact of 6.1 in the worst case.
  @cite_6: Many problems at the intersection of combinatorics and computer science require solving for a permutation that optimally matches, ranks, or sorts some data. These problems usually have a task-specific, often non-differentiable objective function that data-driven algorithms can use as a learning signal. In this paper, we propose the Sinkhorn Policy Gradient (SPG) algorithm for learning policies on permutation matrices. The actor-critic neural network architecture we introduce for SPG uniquely decouples representation learning of the state space from the highly-structured action space of permutations with a temperature-controlled Sinkhorn layer. The Sinkhorn layer produces continuous relaxations of permutation matrices so that the actor-critic architecture can be trained end-to-end. Our empirical results show that agents trained with SPG can perform competitively on sorting, the Euclidean TSP, and matching tasks. We also observe that SPG is significantly more data efficient at the matching task than the baseline methods, which indicates that SPG is conducive to learning representations that are useful for reasoning about permutations.
summary: The work presented in @cite_6 uses an actor-critic based learning on permutation matrices. Authors target combinatorial problems that coincide with graph theory such as Maximum Weight Matching problem (MWM). Authors rely on GRU structures for representation learning over all possible match pairs in a given graph after non-linear embeddings followed by an outer dot product for pairwise correlation mappings. The actor-network maximizes the average reward by choosing the deterministic action @math generated by the network and with the reward obtained from the critic net @math .