A path-level regret bound for PathUCB that decomposes regret over suboptimal paths via a per-path complexity C(pi) combining each edge's prefix and suffix reliability, complementary to the edge-level CCB bound and more informative on structured graphs with polynomially many source-to-goal paths.
Abstract
We introduce Stochastic Reset Pathfinding (SRP), an episodic learning problem on a known directed graph with unknown stationary edge success probabilities. In each episode, the agent commits to a source-to-goal path, and any edge failure during execution resets it to the source. SRP captures settings such as entanglement distribution in quantum repeater networks, payment routing on the Lightning Network, and delivery in unreliable mesh networks. We show that the global-reset structure makes the optimal policy open-loop, placing SRP within the combinatorial cascading bandit (CCB) framework. We propose a Log-Dijkstra meta-algorithm with UCB (PathUCB) and Thompson Sampling (PathTS) instantiations. Our main technical result is a path-level regret bound for PathUCB that decomposes regret over suboptimal paths via a per-path complexity C(pi) combining each edge's prefix and suffix reliability. The bound is complementary to the edge-level CCB bound and more informative on structured graphs with polynomially many source-to-goal paths. Experiments on quantum-network, layered-DAG, grid-world, and Erdos-Renyi domains support the theory and show that PathTS typically achieves the best empirical performance among the algorithms tested. We then exhibit an adversarial instance on which PathTS fails to converge, consistent with a known exponential obstruction for combinatorial Thompson Sampling on multiplicative-reward problems. We recommend PathTS as the practical default while cautioning that adversarial instances exist.
We study stochastic multi-armed bandits on dynamic graphs, where arms correspond to the vertices of a network with time-varying edges. In this setting, the learner is restricted to local movement, selecting only its current node or an immediate neighbor at each round. This constraint decouples best-arm identification from exploitation: even after the optimal arm is identified, the learner may remain unable to reach it through the evolving topology. We identify a process-agnostic structural condition, based on sliding-window mixing, that ensures the graph's intrinsic walk remains stable for both exploration and navigation. Under this regime, we analyze a family of local explore-then-commit algorithms and establish sublinear expected regret. Our framework includes a reward-aware strategy, for which we prove a worst-case safety theorem and a separate performance gain theorem.
Sourav Chakraborty, Amit Kiran Rege, C. Monteleoni et al.· 0 citations
Reconstructing an unknown graph from the trajectory of a random walk arises both for spatial correlation networks in astrophysics and for connectivity inference in network science. We present a reconstruction pipeline whose observable is the random-walk co-visitation matrix, whose model is a pairwise edge-weight basis, and whose fitter is a frame-balanced Levenberg-Marquardt (fbLM) scheme with per-node group weights and a self-calibrated edge readout. Unlike the marginal occupation, the co-visitation retains the ordered pair before the row sum is taken, and the pairwise basis can represent structure that an additive node-potential model cannot; neither change suffices alone. We apply the pipeline to an email communication subgraph, to Delaunay and Voronoi networks built from a COSMOS sky catalogue, and to two controlled 12-vertex test graphs, one unicyclic and one a tree, under both analytic-noise and finite-walk regimes. Reconstructions are scored against the ground-truth adjacency, which enters nowhere in the fit, by true/false positives and the Matthews correlation coefficient (MCC). All test-beds are reconstructed with high fidelity at full graph size: on finite-walk data we recover the COSMOS Delaunay and Voronoi graphs at MCC above 0.98 up to their full extent, N=119 and N=223, the whole graph rather than a cut-out of it, and the empirical email-Eu-core graph at N=240 (417 edges). On the full Delaunay graph a graphical-lasso reference returns MCC 0.540 against 0.988 for fbLM. Each reconstructed edge carries a Fisher-propagated uncertainty, and the residual misses are almost entirely confined to edges the walk never traverses. In the finite-walk regime the limiting factor is therefore walk coverage rather than the fit: essentially every edge the walk visits is recovered, so reconstructibility is governed by the sampling of the graph rather than by the estimator.
This work forms a correction-aware network model that tracks susceptible, exposed, infectious, and corrected agents and derive its early-invasion condition for heterogeneous communication networks, and couple this propagation model to an analytic majority-vote benchmark in which a clean-task reliability target imposes a minimum connectivity requirement.
GraphRoute-Transfer, a graph-neural-network policy that assigns per-node timers from local structural features and is by construction permutation- and size-invariant, is proposed, a graph-neural-network policy that assigns per-node timers from local structural features and is by construction permutation- and size-invariant.
Yuto Nakamura· Journal of Computing and Ele...· 0 citations
Influence maximization seeks a limited seed set that maximizes diffusion spread. Topology-based rankings are efficient but often ignore finite-horizon dynamics and seed-set redundancy, whereas simulation-assisted greedy methods can be computationally expensive. To balance effectiveness, efficiency, and interpretability, this paper proposes temporal multi-path marginal coverage (TMPMC), a deterministic surrogate for finite-horizon susceptible–infected–recovered (SIR) influence maximization. TMPMC estimates source–target probabilities through temporal path propagation, global noisy-OR aggregation over retained paths, and target-level marginal coverage. Unlike IC- or LT-oriented path approximations, TMPMC accounts for repeated infection attempts, recovery risk, feasible arrival times, and a finite propagation horizon. Its monotonicity and submodularity results apply to the surrogate objective, not to the exact stochastic SIR expectation. Across 1,000 common-random-number SIR possible worlds, TMPMC obtains a higher paired AUC than the strongest ranking or heuristic reference on all twelve networks, with an average relative gain of 6.39%. Comparisons with the same-model CELF++ reference, finite-depth IC-based cross-model RR references, and adapted learning-based references reveal a network-dependent effectiveness–efficiency trade-off rather than uniform dominance. High-precision diagnostics show strong within-budget and within-base candidate ranking fidelity, while diffusion-parameter, propagation-horizon, and unified single-thread time–memory analyses characterize robustness and computational scaling. These results support TMPMC as a training-free and interpretable surrogate when finite-horizon SIR-aware seed ranking is required.
Tianyi Zhang, Baojun Fu· Journal of King Saud Univers...· 0 citations
Learning-based methods for the traveling salesman problem (TSP) are often evaluated through the tours produced after decoding or search, but the learned object itself frequently lives in a surrogate space such as heatmaps, assignments, construction policies, or search-guidance scores. This hides the fundamental question: what Hamiltonian structure has actually been learned before decoding? In this study, we directly answer this question by learning TSP through a structurally meaningful latent object, rather than leaving most of the Hamiltonian structure to the final decoding stage. Based on a connected-by-construction rooted $1$-tree Gibbs family, we propose an end-to-end unsupervised learning pipeline called \emph{C2TSP}. The pipeline learns residual edge perturbations from unbiased TSP cost through implicit differentiation. For structural correction, a smoothed Held--Karp layer restores expected degree balance, while certificate-guided sharpening further pushes the connected distribution toward more tour-like structures. Experiments show that C2TSP yields strong decoding performance while preserving interpretable structural information. Ablations further verify that edge perturbation and certificate-guided sharpening jointly improve both tour cost and tour-like structure.