ML models call for an equitable model valuation method to price them. In particular, we investigate the black-box access setting which allows querying a model (to observe predictions) without disclosing model-specific information (e.g., architecture and parameters). By exploiting a Dirichlet abstraction of a model's predictions, we propose a novel and equitable model valuation method called

The performance of Large Language Models is influenced by their characteristics such as architecture, model sizes, decoding methods and so on. Due to differences in structure or function, the weights in different layers of large models have varying distributions. This paper explores the correlations between different types of layers in terms of weights distribution and studies the potential impact of these correlations on LoRA training effectiveness. Firstly, the study reveals that in the model the cosine distances between weights of different layers manifest power-law distribution. We extract Query-projection, down-projection and other weight matrices from the self-attention layers and MLP layers, calculate the singular values of the matrices using singular value decomposition, and organize a certain number of singular values into matrices according to projection's type. By analyzing the probability distribution of the cosine distances between these matrices, it is found that the cosine distances values between them have distinct power-law distribution characteristics. Secondly, based on the results of distance calculations and analysis across different layers of model, a qualitative method is proposed to describe the distribution characteristics of different models. Next, to construct weights that align with the distribution characteristics, a data generator is designed using a combination of Gaussian process and Pareto distribution functions. The generator is used to simulate the generation of data that aligns with specific distribution characteristics. Finally, based on the aforementioned distribution characteristics and data generation method, the weights in LoRA initialization are reshaped for training. Experimental results indicate that, without altering the model structure or training process, this method achieves a certain improvement in the performance of LoRA training.

Value factorisation is a useful technique for multi-agent reinforcement learning (MARL) in global reward game, however, its underlying mechanism is not yet fully understood. This paper studies a theoretical framework for value factorisation with interpretability via Shapley value theory. We generalise Shapley value to Markov convex game called Markov Shapley value (MSV) and apply it as a value factorisation method in global reward game, which is obtained by the equivalence between the two games. Based on the properties of MSV, we derive Shapley-Bellman optimality equation (SBOE) to evaluate the optimal MSV, which corresponds to an optimal joint deterministic policy. Furthermore, we propose Shapley-Bellman operator (SBO) that is proved to solve SBOE.

The generalization ability of Deep Neural Networks (DNNs) is still not fully understood, despite numerous theoretical and empirical analyses. Recently, Allen-Zhu & Li (2023) introduced the concept of multi-views to explain the generalization ability of DNNs, but their main target is ensemble or distilled models, and no method for estimating multi-views used in a prediction of a specific input is discussed. In this paper, we propose Minimal Sufficient Views (MSVs), which is similar to multi-views but can be efficiently computed for real images. MSVs is a set of minimal and distinct features in an input, each of which preserves a model's prediction for the input. We empirically show that there is a clear relationship between the number of MSVs and prediction accuracy across models, including convolutional and transformer models, suggesting that a multi-view like perspective is also important for understanding the generalization ability of (non-ensemble or non-distilled) DNNs.

Keeping risk under control is often more crucial than maximizing expected rewards in real-world decision-making situations, such as finance, robotics, autonomous driving, etc. The most natural choice of risk measures is variance, which penalizes the upside volatility as much as the downside part. Instead, the (downside) semivariance, which captures the negative deviation of a random variable under its mean, is more suitable for risk-averse proposes. This paper aims at optimizing the mean-semivariance (MSV) criterion in reinforcement learning w.r.t. steady reward distribution. Since semivariance is time-inconsistent and does not satisfy the standard Bellman equation, the traditional dynamic programming methods are inapplicable to MSV problems directly. To tackle this challenge, we resort to Perturbation Analysis (PA) theory and establish the performance difference formula for MSV. We reveal that the MSV problem can be solved by iteratively solving a sequence of RL problems with a policy-dependent reward function. Further, we propose two on-policy algorithms based on the policy gradient theory and the trust region method. Finally, we conduct diverse experiments from simple bandit problems to continuous control tasks in MuJoCo, which demonstrate the effectiveness of our proposed methods.

Keeping risk under control is often more crucial than maximizing expected reward in real-world decision-making situations, such as finance, robotics, autonomous driving, etc. The most natural choice of risk measures is variance, while it penalizes the upside volatility as much as the downside part. Instead, the (downside) semivariance, which captures the negative deviation of a random variable under its mean, is more suitable for risk-averse proposes. This paper aims at optimizing the mean-semivariance (MSV) criterion in reinforcement learning w.r.t. steady rewards. Since semivariance is time-inconsistent and does not satisfy the standard Bellman equation, the traditional dynamic programming methods are inapplicable to MSV problems directly. To tackle this challenge, we resort to the Perturbation Analysis (PA) theory and establish the performance difference formula for MSV. We reveal that the MSV problem can be solved by iteratively solving a sequence of RL problems with a policy-dependent reward function. Further, we propose two on-policy algorithms based on the policy gradient theory and the trust region method. Finally, we conduct diverse experiments from simple bandit problems to continuous control tasks in MuJoCo, which demonstrate the effectiveness of our proposed methods.