Under the new analysis, to achieve an -stationary point of the nested problem, it requiresO( 2)samples in total.

Foreacharma, letr(a) and cj(a) be, resp., the meanrewardandmeanresource-j consumption,i.e.,(r(a);c1(a),..., cd(a)):=Eo Da[o].We sometimeswriter =( r(a): a 2 [K])andcj =( cj(a): a 2 [K])asvectorsoverarms. Second, weuseatighterversionof Eq. (3.6) (see AppendixD.3):

Unlike projection based algorithms [14,32] though, momentum does not perform well with FW.

This work aims to learn the directed acyclic graph (DAG) that captures the instantaneous dependencies underlying a multivariate time series. The observed data follow a linear structural vector autoregressive model (SVARM) with both instantaneous and time-lagged dependencies, where the instantaneous structure is modeled by a DAG to reflect potential causal relationships. While recent continuous relaxation approaches impose acyclicity through smooth constraint functions involving powers of the adjacency matrix, they lead to non-convex optimization problems that are challenging to solve. In contrast, we assume that the underlying DAG has only non-negative edge weights, and leverage this additional structure to impose acyclicity via a convex constraint. This enables us to cast the problem of non-negative DAG recovery from multivariate time-series data as a convex optimization problem in abstract form, which we solve using the method of multipliers. Crucially, the convex formulation guarantees global optimality of the solution. Finally, we assess the performance of the proposed method on synthetic time-series data, where it outperforms existing alternatives.

Spectral GNNs, like ChebyNet, are limited by heterophily and over-smoothing due to their static, low-pass filter design. This work investigates the "Adaptive Orthogonal Polynomial Filter" (AOPF) class as a solution. We introduce two models operating in the [-1, 1] domain: 1) `L-JacobiNet`, the adaptive generalization of `ChebyNet` with learnable alpha, beta shape parameters, and 2) `S-JacobiNet`, a novel baseline representing a LayerNorm-stabilized static `ChebyNet`. Our analysis, comparing these models against AOPFs in the [0, infty) domain (e.g., `LaguerreNet`), reveals critical, previously unknown trade-offs. We find that the [0, infty) domain is superior for modeling heterophily, while the [-1, 1] domain (Jacobi) provides superior numerical stability at high K (K>20). Most significantly, we discover that `ChebyNet`'s main flaw is stabilization, not its static nature. Our static `S-JacobiNet` (ChebyNet+LayerNorm) outperforms the adaptive `L-JacobiNet` on 4 out of 5 benchmark datasets, identifying `S-JacobiNet` as a powerful, overlooked baseline and suggesting that adaptation in the [-1, 1] domain can lead to overfitting.

Spectral Graph Neural Networks (GNNs) suffer from two critical limitations: poor performance on "heterophilic" graphs and performance collapse at high polynomial degrees (K), known as over-smoothing. Both issues stem from the static, low-pass nature of standard filters (e.g., ChebyNet). While adaptive polynomial filters, such as the discrete MeixnerNet, have emerged as a potential unified solution, their extension to the continuous domain and stability with unbounded coefficients remain open questions. In this work, we propose `LaguerreNet`, a novel GNN filter based on continuous Laguerre polynomials. `LaguerreNet` learns the filter's spectral shape by making its core alpha parameter trainable, thereby advancing the adaptive polynomial approach. We solve the severe O(k^2) numerical instability of these unbounded polynomials using a `LayerNorm`-based stabilization technique. We demonstrate experimentally that this approach is highly effective: 1) `LaguerreNet` achieves state-of-the-art results on challenging heterophilic benchmarks. 2) It is exceptionally robust to over-smoothing, with performance peaking at K=10, an order of magnitude beyond where ChebyNet collapses.

Spectral Graph Neural Networks (GNNs) based on polynomial filters, such as ChebyNet, suffer from two critical limitations: 1) performance collapse on "heterophilic" graphs and 2) performance collapse at high polynomial degrees (K), known as over-smoothing. Both issues stem from the static, low-pass nature of standard filters. In this work, we propose `KrawtchoukNet`, a GNN filter based on the discrete Krawtchouk polynomials. We demonstrate that `KrawtchoukNet` provides a unified solution to both problems through two key design choices. First, by fixing the polynomial's domain N to a small constant (e.g., N=20), we create the first GNN filter whose recurrence coefficients are \textit{inherently bounded}, making it exceptionally robust to over-smoothing (achieving SOTA results at K=10). Second, by making the filter's shape parameter p learnable, the filter adapts its spectral response to the graph data. We show this adaptive nature allows `KrawtchoukNet` to achieve SOTA performance on challenging heterophilic benchmarks (Texas, Cornell), decisively outperforming standard GNNs like GAT and APPNP.

Remarkable capabilities have been achieved by robotics and AI, mastering complex tasks and environments. Yet, humans often remain passive observers, fascinated but uncertain how to engage. Robots, in turn, cannot reach their full potential in human-populated environments without effectively modeling human states and intentions and adapting their behavior. To achieve a synergistic human-robot collaboration (HRC), a continuous information flow should be established: humans must intuitively communicate instructions, share expertise, and express needs. In parallel, robots must clearly convey their internal state and forthcoming actions to keep users informed, comfortable, and in control. This review identifies and connects key components enabling intuitive information exchange and skill transfer between humans and robots. We examine the full interaction pipeline: from the human-to-robot communication bridge translating multimodal inputs into robot-understandable representations, through adaptive planning and role allocation, to the control layer and feedback mechanisms to close the loop. Finally, we highlight trends and promising directions toward more adaptive, accessible HRC.