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The impact of softmax on the value function itself in reinforcement learning (RL) is often viewed as problematic because it leads to sub-optimal value (or Q) functions and interferes with the contraction properties of the Bellman operator.…

Machine Learning · Computer Science 2019-05-21 Zhao Song , Ronald E. Parr , Lawrence Carin

Learning complicated value functions in high dimensional state space by function approximation is a challenging task, partially due to that the max-operator used in temporal difference updates can theoretically cause instability for most…

Machine Learning · Computer Science 2020-12-21 Yaozhong Gan , Zhe Zhang , Xiaoyang Tan

Policy-gradient approaches to reinforcement learning have two common and undesirable overhead procedures, namely warm-start training and sample variance reduction. In this paper, we describe a reinforcement learning method based on a…

Machine Learning · Computer Science 2017-10-17 Nan Ding , Radu Soricut

Value function estimation is an important task in reinforcement learning, i.e., prediction. The Boltzmann softmax operator is a natural value estimator and can provide several benefits. However, it does not satisfy the non-expansion…

Machine Learning · Computer Science 2019-09-10 Ling Pan , Qingpeng Cai , Qi Meng , Wei Chen , Longbo Huang , Tie-Yan Liu

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…

Machine Learning · Computer Science 2021-12-24 Shaoshi Sun , Zhenyuan Zhang , BoCheng Huang , Pengbin Lei , Jianlin Su , Shengfeng Pan , Jiarun Cao

In this paper, we utilize results from convex analysis and monotone operator theory to derive additional properties of the softmax function that have not yet been covered in the existing literature. In particular, we show that the softmax…

Optimization and Control · Mathematics 2018-08-23 Bolin Gao , Lacra Pavel

This paper proposes a novel fuzzy action selection method to leverage human knowledge in reinforcement learning problems. Based on the estimates of the most current action-state values, the proposed fuzzy nonlinear mapping as-signs each…

Artificial Intelligence · Computer Science 2021-06-15 Mohsen Annabestani , Ali Abedi , Mohammad Reza Nematollahi , Mohammad Bagher Naghibi Sis-tani

A key property of reasoning systems is the ability to make sharp decisions on their input data. For contemporary AI systems, a key carrier of sharp behaviour is the softmax function, with its capability to perform differentiable query-key…

Machine Learning · Computer Science 2025-06-03 Petar Veličković , Christos Perivolaropoulos , Federico Barbero , Razvan Pascanu

Softmax is popular normalization method used in machine learning. Deep learning solutions like Transformer or BERT use the softmax function intensively, so it is worthwhile to optimize its performance. This article presents our methodology…

Mathematical Software · Computer Science 2019-05-28 Jacek Czaja , Michal Gallus , Tomasz Patejko , Jian Tang

The softmax function is a fundamental component in deep learning. This study delves into the often-overlooked parameter within the softmax function, known as "temperature," providing novel insights into the practical and theoretical aspects…

Machine Learning · Computer Science 2025-03-03 Hao Xuan , Bokai Yang , Xingyu Li

SoftMax is a ubiquitous ingredient of modern machine learning algorithms. It maps an input vector onto a probability simplex and reweights the input by concentrating the probability mass at large entries. Yet, as a smooth approximation to…

Machine Learning · Computer Science 2025-01-09 Yuxuan Zhou , Mario Fritz , Margret Keuper

In recent years, the softmax model and its fast approximations have become the de-facto loss functions for deep neural networks when dealing with multi-class prediction. This loss has been extended to language modeling and recommendation,…

Machine Learning · Statistics 2019-09-19 Ugo Tanielian , Flavian Vasile

Reinforcement learning (RL) agents can leverage batches of previously collected data to extract a reasonable control policy. An emerging issue in this offline RL setting, however, is that the bootstrapping update underlying many of our…

Machine Learning · Computer Science 2023-04-20 Chenjun Xiao , Han Wang , Yangchen Pan , Adam White , Martha White

In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately,…

Machine Learning · Computer Science 2021-03-01 Elita A. Lobo , Mohammad Ghavamzadeh , Marek Petrik

Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized…

Econometrics · Economics 2026-04-01 Justin Whitehouse , Qizhao Chen , Morgane Austern , Vasilis Syrgkanis

A soft-max function has two main efficiency measures: (1) approximation - which corresponds to how well it approximates the maximum function, (2) smoothness - which shows how sensitive it is to changes of its input. Our goal is to identify…

Machine Learning · Computer Science 2026-01-01 Alessandro Epasto , Mohammad Mahdian , Vahab Mirrokni , Manolis Zampetakis

Transformers have transformed the field of natural language processing. This performance is largely attributed to the use of stacked self-attention layers, each of which consists of matrix multiplies as well as softmax operations. As a…

Hardware Architecture · Computer Science 2021-03-18 Jacob R. Stevens , Rangharajan Venkatesan , Steve Dai , Brucek Khailany , Anand Raghunathan

Nowadays artificial neural network models achieve remarkable results in many disciplines. Functions mapping the representation provided by the model to the probability distribution are the inseparable aspect of deep learning solutions.…

Machine Learning · Computer Science 2023-04-24 Klaudia Bałazy , Łukasz Struski , Marek Śmieja , Jacek Tabor

We propose DropMax, a stochastic version of softmax classifier which at each iteration drops non-target classes according to dropout probabilities adaptively decided for each instance. Specifically, we overlay binary masking variables over…

Machine Learning · Computer Science 2018-11-05 Hae Beom Lee , Juho Lee , Saehoon Kim , Eunho Yang , Sung Ju Hwang

Despite achieving state-of-the-art results in nearly all Natural Language Processing applications, fine-tuning Transformer-based language models still requires a significant amount of labeled data to work. A well known technique to reduce…

Machine Learning · Computer Science 2025-03-13 Julius Gonsior , Christian Falkenberg , Silvio Magino , Anja Reusch , Maik Thiele , Wolfgang Lehner
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