Under/overestimation of state/action values are harmful for reinforcement learning agents. In this paper, we show that a state/action value estimated using the Bellman equation can be decomposed to a weighted sum of path-wise values that follow log-normal distributions. Since log-normal distributions are skewed, the distribution of estimated state/action values can also be skewed, leading to an imbalanced likelihood of under/overestimation. The degree of such imbalance can vary greatly among actions and policies within a single problem instance, making the agent prone to select actions/policies that have inferior expected return and higher likelihood of overestimation. We present a comprehensive analysis to such skewness, examine its factors and impacts through both theoretical and empirical results, and discuss the possible ways to reduce its undesirable effects.

Under/overestimation of state/action values are harmful for reinforcement learning agents. In this paper, we show that a state/action value estimated using the Bellman equation can be decomposed to a weighted sum of path-wise values that follow log-normal distributions. Since log-normal distributions are skewed, the distribution of estimated state/action values can also be skewed, leading to an imbalanced likelihood of under/overestimation. The degree of such imbalance can vary greatly among actions and policies within a single problem instance, making the agent prone to select actions/policies that have inferior expected return and higher likelihood of overestimation. We present a comprehensive analysis to such skewness, examine its factors and impacts through both theoretical and empirical results, and discuss the possible ways to reduce its undesirable effects.

Under/overestimation of state/action values are harmful for reinforcement learning agents.

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter-Syntetos-Babai (TSB) method provide simple heuristics but lack a principled generative foundation. Deep learning models address these limitations but often require large datasets and sacrifice interpretability. We introduce TSB-HB, a hierarchical Bayesian extension of TSB. Demand occurrence is modeled with a Beta-Binomial distribution, while nonzero demand sizes follow a Log-Normal distribution. Crucially, hierarchical priors enable partial pooling across items, stabilizing estimates for sparse or cold-start series while preserving heterogeneity. This framework yields a fully generative and interpretable model that generalizes classical exponential smoothing. On the UCI Online Retail dataset, TSB-HB achieves lower RMSE and RMSSE than Croston, SBA, TSB, ADIDA, IMAPA, ARIMA and Theta, and on a subset of the M5 dataset it outperforms all classical baselines we evaluate. The model provides calibrated probabilistic forecasts and improved accuracy on intermittent and lumpy items by combining a generative formulation with hierarchical shrinkage, while remaining interpretable and scalable.

Traffic flow forecasting is essential for managing congestion, improving safety, and optimizing various transportation systems. However, it remains a prevailing challenge due to the stochastic nature of urban traffic and environmental factors. Better predictions require models capable of accommodating the traffic variability influenced by multiple dynamic and complex interdependent factors. In this work, we propose a Graph Neural Network (GNN) framework to address the stochasticity by leveraging adaptive adjacency matrices using log-normal distributions and Coefficient of Variation (CV) values to reflect real-world travel time variability. Additionally, weather factors such as temperature, wind speed, and precipitation adjust edge weights and enable GNN to capture evolving spatio-temporal dependencies across traffic stations. This enhancement over the static adjacency matrix allows the model to adapt effectively to traffic stochasticity and changing environmental conditions. Furthermore, we utilize the Adaptive Conformal Prediction (ACP) framework to provide reliable uncertainty quantification, achieving target coverage while maintaining acceptable prediction intervals. Experimental results demonstrate that the proposed model, in comparison with baseline methods, showed better prediction accuracy and uncertainty bounds. We, then, validate this method by constructing traffic scenarios in SUMO and applying Monte-Carlo simulation to derive a travel time distribution for a Vehicle Under Test (VUT) to reflect real-world variability. The simulated mean travel time of the VUT falls within the intervals defined by INRIX historical data, verifying the model's robustness.

Generative conversational interfaces powered by large language models (LLMs) typically stream output token-by-token at a rate determined by computational budget, often neglecting actual human reading speeds and the cognitive load associated with the content. This mismatch frequently leads to inefficient use of computational resources. For example, in cloud-based services, streaming content faster than users can read appears unnecessary, resulting in wasted computational resources and potential delays for other users, particularly during peak usage periods. To address this issue, we propose an adaptive streaming method that dynamically adjusts the pacing of LLM streaming output in real-time based on inferred cognitive load. Our approach estimates the cognitive load associated with streaming content and strategically slows down the stream during complex or information-rich segments, thereby freeing computational resources for other users. We conducted a statistical analysis and simulation based on a statistical model derived from data collected in a crowdsourced user study across various types of LLM-generated content. Our results show that this adaptive method can effectively reduce computational consumption while largely maintaining streaming speed above user's normal reading speed.

Developing algorithms for real-life problems that perform well in practice highly depends on the availability of realistic data for testing. Obtaining real-life data for optimization problems in health care, however, is often difficult. This is especially true for any patient related optimization problems, e.g., for patient-to-room assignment, due to data privacy policies. Furthermore, obtained real-life data usually cannot be published which prohibits reproducibility of results by other researchers. Therefore, often artificially generated instances are used. We use these insights to develop a configurable instance generator for PRA with an easy-to-use graphical user interface. Configurability is in this case especially important as we observed in an extensive analysis of real-life data that, e.g., the probability distribution for patients' age and length of stay depends on the respective ward. Introduction The development of algorithms for real-world optimization problems that perform well in practice heavily relies on the availability of realistic data for testing.

Studies in neuroscience have shown that biological synapses follow a log-normal distribution whose transitioning can be explained by noisy multiplicative dynamics. Biological networks can function stably even under dynamically fluctuating conditions arising due to unreliable synaptic transmissions. Here we ask: Is it possible to design similar multiplicative training in artificial neural networks? To answer this question, we derive a Bayesian learning rule that assumes log-normal posterior distributions over weights which gives rise to a new Log-Normal Multiplicative Dynamics (LMD) algorithm. The algorithm uses multiplicative updates with both noise and regularization applied multiplicatively. The method is as easy to implement as Adam and only requires one additional vector to store. Our results show that LMD achieves stable and accurate training-from-scratch under low-precision forward operations for Vision Transformer and GPT-2. These results suggest that multiplicative dynamics, a biological feature, may enable stable low-precision inference and learning on future energy-efficient hardware.

The variational autoencoder (VAE) is a simple and efficient generative artificial intelligence method for modeling complex probability distributions of various types of data, such as images and texts. However, it suffers some main shortcomings, such as lack of interpretability in the latent variables, difficulties in tuning hyperparameters while training, producing blurry, unrealistic downstream outputs or loss of information due to how it calculates loss functions and recovers data distributions, overfitting, and origin gravity effect for small data sets, among other issues. These and other limitations have caused unsatisfactory generation effects for the data with complex distributions. In this work, we proposed and developed a polynomial hierarchical variational autoencoder (PH-VAE), in which we used a polynomial hierarchical date format to generate or to reconstruct the data distributions. In doing so, we also proposed a novel Polynomial Divergence in the loss function to replace or generalize the Kullback-Leibler (KL) divergence, which results in systematic and drastic improvements in both accuracy and reproducibility of the re-constructed distribution function as well as the quality of re-constructed data images while keeping the dataset size the same but capturing fine resolution of the data. Moreover, we showed that the proposed PH-VAE has some form of disentangled representation learning ability.

Under/overestimation of state/action values are harmful for reinforcement learning agents. In this paper, we show that a state/action value estimated using the Bellman equation can be decomposed to a weighted sum of path-wise values that follow log-normal distributions. Since log-normal distributions are skewed, the distribution of estimated state/action values can also be skewed, leading to an imbalanced likelihood of under/overestimation. The degree of such imbalance can vary greatly among actions and policies within a single problem instance, making the agent prone to select actions/policies that have inferior expected return and higher likelihood of overestimation. We present a comprehensive analysis to such skewness, examine its factors and impacts through both theoretical and empirical results, and discuss the possible ways to reduce its undesirable effects.