Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose approximate bilinear programming, a new formulation of value function approximation that provides strong a priori guarantees. In particular, it provably finds an approximate value function that minimizes the Bellman residual. Solving a bilinear program optimally is NP hard, but this is unavoidable because the Bellman-residual minimization itself is NP hard. We, therefore, employ and analyze a common approximate algorithm for bilinear programs.

Fitted value iteration (FVI) with ordinary least squares regression is known to diverge. We present a new method, "Expansion-Constrained Ordinary Least Squares" (ECOLS), that produces a linear approximation but also guarantees convergence when used with FVI. To ensure convergence, we constrain the least squares regression operator to be a non-expansion in the infinity-norm. We show that the space of function approximators that satisfy this constraint is more rich than the space of "averagers," we prove a minimax property of the ECOLS residual error, and we give an efficient algorithm for computing the coefficients of ECOLS based on constraint generation. We illustrate the algorithmic convergence of FVI with ECOLS in a suite of experiments, and discuss its properties.

Hashing is a common method to reduce large, potentially infinite feature vectors to a fixed-size table. In reinforcement learning, hashing is often used in conjunction with tile coding to represent states in continuous spaces. Hashing is also a promising approach to value function approximation in large discrete domains such as Go and Hearts, where feature vectors can be constructed by exhaustively combining a set of atomic features. Unfortunately, the typical use of hashing in value function approximation results in biased value estimates due to the possibility of collisions. Recent work in data stream summaries has led to the development of the tug-of-war sketch, an unbiased estimator for approximating inner products.

Classical results in neural network approximation theory show how arbitrary continuous functions can be approximated by networks with a single hidden layer, under mild assumptions on the activation function. However, the classical theory does not give a constructive means to generate the network parameters that achieve a desired accuracy. Recent results have demonstrated that for specialized activation functions, such as ReLUs and some classes of analytic functions, high accuracy can be achieved via linear combinations of randomly initialized activations. These recent works utilize specialized integral representations of target functions that depend on the specific activation functions used. This paper defines mollified integral representations, which provide a means to form integral representations of target functions using activations for which no direct integral representation is currently known. The new construction enables approximation guarantees for randomly initialized networks for a variety of widely used activation functions.

Function approximation (FA) has been a critical component in solving large zero-sum games. Yet, little attention has been given towards FA in solving \textit{general-sum} extensive-form games, despite them being widely regarded as being computationally more challenging than their fully competitive or cooperative counterparts. A key challenge is that for many equilibria in general-sum games, no simple analogue to the state value function used in Markov Decision Processes and zero-sum games exists. In this paper, we propose learning the \textit{Enforceable Payoff Frontier} (EPF) -- a generalization of the state value function for general-sum games. We approximate the optimal \textit{Stackelberg extensive-form correlated equilibrium} by representing EPFs with neural networks and training them by using appropriate backup operations and loss functions. This is the first method that applies FA to the Stackelberg setting, allowing us to scale to much larger games while still enjoying performance guarantees based on FA error. Additionally, our proposed method guarantees incentive compatibility and is easy to evaluate without having to depend on self-play or approximate best-response oracles.

Event detection (ED) from sequences of data is a critical challenge in various fields, including surveillance [Clavel et al., 2005], multimedia processing [Xiang and Wang, 2019, Lai, 2022], and social network analysis [Cordeiro and Gama, 2016]. Neural network-based architectures have been developed for ED, leveraging various data types such as text, images, social media data, and audio. Integrating commonsense and structural knowledge about events and their relationships can significantly enhance machine learning methods for ED. For example, in analyzing a soccer match video, the knowledge that a red card shown to a player is typically followed by the player leaving the field can aid in event detection. Additionally, knowledge about how simple events compose complex events is also useful for complex event detection. Background knowledge has been shown to improve the detection of complex events especially when training data is limited [Yin et al., 2020].

The beekeeping sector has undergone considerable production variations over the past years due to adverse weather conditions, occurring more frequently as climate change progresses. These phenomena can be high-impact and cause the environment to be unfavorable to the bees' activity. We disentangle the honey production drivers with tree-based methods and predict honey production variations for hives in Italy, one of the largest honey producers in Europe. The database covers hundreds of beehive data from 2019-2022 gathered with advanced precision beekeeping techniques. We train and interpret the machine learning models making them prescriptive other than just predictive. Superior predictive performances of tree-based methods compared to standard linear techniques allow for better protection of bees' activity and assess potential losses for beekeepers for risk management.

Swarm Intelligence algorithms have gained significant attention in recent years as a means of solving complex and non-deterministic problems. These algorithms are inspired by the collective behavior of natural creatures, and they simulate this behavior to develop intelligent agents for computational tasks. One such algorithm is Ant Colony Optimization (ACO), which is inspired by the foraging behavior of ants and their pheromone laying mechanism. ACO is used for solving difficult problems that are discrete and combinatorial in nature. Part-of-Speech (POS) tagging is a fundamental task in natural language processing that aims to assign a part-of-speech role to each word in a sentence. In this research paper, proposed a high-performance POS-tagging method based on ACO called ACO-tagger. This method achieved a high accuracy rate of 96.867%, outperforming several state-of-the-art methods. The proposed method is fast and efficient, making it a viable option for practical applications.

A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable artificial intelligence and machine learning). In this research, new concepts of rough randomness that are neither stochastic nor based on properties of strings are introduced by the present author. Her concepts are intended to capture a wide variety of rough processes (applicable to both static and dynamic data), construct related models, and explore the validity of other machine learning algorithms. The last mentioned is restricted to soft/hard clustering algorithms in this paper. Two new computationally efficient algebraically-justified algorithms for soft and hard cluster validation that involve rough random functions are additionally proposed in this research. A class of rough random functions termed large-minded reasoners have a central role in these.

Predicting body fat can provide medical practitioners and users with essential information for preventing and diagnosing heart diseases. Hybrid machine learning models offer better performance than simple regression analysis methods by selecting relevant body measurements and capturing complex nonlinear relationships among selected features in modelling body fat prediction problems. There are, however, some disadvantages to them. Current machine learning. Modelling body fat prediction as a combinatorial single- and multi-objective optimisation problem often gets stuck in local optima. When multiple feature subsets produce similar or close predictions, avoiding local optima becomes more complex. Evolutionary feature selection has been used to solve several machine-learning-based optimisation problems. A fuzzy set theory determines appropriate levels of exploration and exploitation while managing parameterisation and computational costs. A weighted-sum body fat prediction approach was explored using evolutionary feature selection, fuzzy set theory, and machine learning algorithms, integrating contradictory metrics into a single composite goal optimised by fuzzy adaptive evolutionary feature selection. Hybrid fuzzy adaptive global learning local search universal diversity-based feature selection is applied to this single-objective feature selection-machine learning framework (FAGLSUD-based FS-ML). While using fewer features, this model achieved a more accurate and stable estimate of body fat percentage than other hybrid and state-of-the-art machine learning models. A multi-objective FAGLSUD-based FS-MLP is also proposed to analyse accuracy, stability, and dimensionality conflicts simultaneously. To make informed decisions about fat deposits in the most vital body parts and blood lipid levels, medical practitioners and users can use a well-distributed Pareto set of trade-off solutions.