Global linear convergence of entropy-regularized softmax policy gradient beyond tabular MDPs

We study the global convergence of policy gradient for infinite-horizon entropy-regularized Markov decision processes (MDPs) with continuous state and action spaces. We consider log-linear softmax policies with linear function approximation, which extend the tabular softmax parameterization while retaining a tractable policy class. Under $Q^π_τ$-realizability for the regularized state-action value function, we first establish a non-uniform Polyak--Łojasiewicz (PŁ) inequality. The non-uniformity arises through degeneracy of constants associated with the policy geometry, namely the Fisher information matrix or an uncentered feature covariance matrix. We then identify two feature regimes under which this non-uniform constant can be bounded along the gradient flow. For full-affine-span features, we prove radial unboundedness of the KL regularizer and show that the smallest eigenvalue of the Fisher information matrix remains bounded below by an initialization-dependent positive constant. For simplex-valued features, we prove an analogous radial unboundedness result in the subspace orthogonal to the all-ones vector and obtain a uniform lower bound for the smallest eigenvalue of the uncentered covariance matrix. These results imply global linear convergence of the regularized objective along the gradient flow, i.e. suboptimality decaying as $\mathcal{O}(e^{-Ct})$ for some $C>0$. Our analysis extends the global convergence theory of entropy-regularized softmax policy gradient beyond the tabular setting of Agarwal et al. (2020); Bhandari and Russo (2024); Mei et al. (2020).

Curriculum Negative Mining For Temporal Networks

Temporal networks are effective in capturing the evolving interactions of networks over time, such as social networks and e-commerce networks. In recent years, researchers have primarily concentrated on developing specific model architectures for Temporal Graph Neural Networks (TGNNs) in order to improve the representation quality of temporal nodes and edges. However, limited attention has been given to the quality of negative samples during the training of TGNNs. When compared with static networks, temporal networks present two specific challenges for negative sampling: positive sparsity and positive shift. Positive sparsity refers to the presence of a single positive sample amidst numerous negative samples at each timestamp, while positive shift relates to the variations in positive samples across different timestamps. To robustly address these challenges in training TGNNs, we introduce Curriculum Negative Mining (CurNM), a model-aware curriculum learning framework that adaptively adjusts the difficulty of negative samples. Within this framework, we first establish a dynamically updated negative pool that balances random, historical, and hard negatives to address the challenges posed by positive sparsity. Secondly, we implement a temporal-aware negative selection module that focuses on learning from the disentangled factors of recently active edges, thus accurately capturing shifting preferences. Extensive experiments on 12 datasets and 3 TGNNs demonstrate that our method outperforms baseline methods by a significant margin. Additionally, thorough ablation studies and parameter sensitivity experiments verify the usefulness and robustness of our approach. Our code is available at https://github.com/zziyue83/CurNM.