Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing procedures for statistical networks based on the principle of maximum entropy (MaxEnt). Our approach formulates a constrained entropy-maximization problem on the space of networks, subject to prescribed structural constraints. The resulting test statistics are defined through the Lagrange multipliers associated with the constrained optimization problem, which, to our knowledge, is novel in the statistical networks literature. We establish consistency in the classical regime where the number of vertices is fixed. We then consider asymptotic regimes in which the graph size grows with the sample size, developing tests for both dense and sparse settings. In the dense case, we analyze exponential random graph models (ERGM) (including the Erdös-Rènyi models), while in the sparse regime our theory applies to Erd{ö}s-R{è}nyi graphs. Our analysis leverages recent advances in nonlinear large deviation theory for random graphs. We further show that the proposed Lagrange-multiplier framework connects naturally to classical score tests for constrained maximum likelihood estimation. The results provide a unified entropy-based framework for network model assessment across diverse growth regimes.

Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations--an inference task also known as source distribution estimation. This problem can be ill-posed, however, since many different source distributions might produce the same distribution of data-consistent simulations. To make a principled choice among many equally valid sources, we propose an approach which targets the maximum entropy distribution, i.e., prioritizes retaining as much uncertainty as possible.

In the policy evaluation steps, the critic is updated to capture the soft Q-function. In the policy improvement steps, the actor is adjusted in accordance with the updated soft Q-function.

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In Distributional Reinforcement Learning (D-RL) [Bellemare et al., 2023], an agent aims to estimate Sutton and Barto, 2018], where the objective is to predict the expected return only. In Section 3, we answer this methodological question, showing that it is possible to reformulate Policy Evaluation in a distributional setting so that its performance index is explicitly intertwined with the representation of the (state or action) spaces.

For a small training set, CNNs behave similarly.

Diffusion models have achieved remarkable success in data-driven learning and in sampling from complex, unnormalized target distributions. Building on this progress, we reinterpret Maximum Entropy Reinforcement Learning (MaxEntRL) as a diffusion model-based sampling problem. We tackle this problem by minimizing the reverse Kullback-Leibler (KL) divergence between the diffusion policy and the optimal policy distribution using a tractable upper bound. By applying the policy gradient theorem to this objective, we derive a modified surrogate objective for MaxEntRL that incorporates diffusion dynamics in a principled way. This leads to simple diffusion-based variants of Soft Actor-Critic (SAC), Proximal Policy Optimization (PPO) and Wasserstein Policy Optimization (WPO), termed DiffSAC, DiffPPO and DiffWPO. All of these methods require only minor implementation changes to their base algorithm. We find that on standard continuous control benchmarks, DiffSAC, DiffPPO and DiffWPO achieve better returns and higher sample efficiency than SAC and PPO.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/