We develop a deeper understanding of its relationship with more conventional analyses of extragradient methods [Nem04, Nes07]. We also give improved solvers for the subproblems required by variants of the [She17] algorithm, designed through the lens of relative smoothness [BBT17, LFN18].

Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MO-COPs).

A promising way to extract computational principles from these large datasets is to train data-constrained recurrent neural networks (dRNNs).

We prove part the first part of the proposition (weak duality) by induction. It is well-known that, by the value iteration algorithm's convergence, Q Consider a state s S and a feasible action a A (s). We use an induction proof. B (w), which follows by the convergence of value iteration.A.2 Proof of Theorem 1 Proof. Now we state the following lemma.

"subagents," one for each subproblem, and then combine their solutions to establish

In the inference process, the submodel is used to solve the corresponding subproblem. The input dimensions of the node features vary with different problems. A masking mechanism is adopted in each decoding step to ensure the solution feasibility. For MOTSP, the visited nodes are masked. NHDE-M usually spends relatively more inference time than MDRL with the same number of weights.

B, which is part of the linear least squares right-hand-side we can solve for.