Federated learning has received great attention for its capability to train a large-scale model in a decentralized manner without needing to access user data directly. It helps protect the users' private data from centralized collecting. Unlike distributed machine learning, federated learning aims to tackle non-IID data from heterogeneous sources in various real-world applications, such as those on smartphones. Existing federated learning approaches usually adopt a single global model to capture the shared knowledge of all users by aggregating their gradients, regardless of the discrepancy between their data distributions. However, due to the diverse nature of user behaviors, assigning users' gradients to different global models (i.e., centers) can better capture the heterogeneity of data distributions across users. Our paper proposes a novel multi-center aggregation mechanism for federated learning, which learns multiple global models from the non-IID user data and simultaneously derives the optimal matching between users and centers. We formulate the problem as a joint optimization that can be efficiently solved by a stochastic expectation maximization (EM) algorithm. Our experimental results on benchmark datasets show that our method outperforms several popular federated learning methods.

The weighted sum method is a simple and widely used technique that scalarizes multiple conflicting objectives into a single objective function. It suffers from the problem of determining the appropriate weights corresponding to the objectives. This paper proposes a novel Hierarchical Bayesian model based on Multinomial distribution and Dirichlet prior to refine the weights for solving such multi-objective route optimization problems. The model and methodologies revolve around data obtained from a small scale pilot survey. The method aims at improving the existing methods of weight determination in the field of Intelligent Transport Systems as data driven choice of weights through appropriate probabilistic modelling ensures, on an average, much reliable results than non-probabilistic techniques. Application of this model and methodologies to simulated as well as real data sets revealed quite encouraging performances with respect to stabilizing the estimates of weights.

The goal of this thesis is to design a learning model predictive controller (LMPC) that allows multiple agents to race competitively on a predefined race track in real-time. This thesis addresses two major shortcomings in the already existing single-agent formulation. Previously, the agent determines a locally optimal trajectory but does not explore the state space, which may be necessary for overtaking maneuvers. Additionally, obstacle avoidance for LMPC has been achieved in the past by using a non-convex terminal set, which increases the complexity for determining a solution to the optimization problem. The proposed algorithm for multi-agent racing explores the state space by executing the LMPC for multiple different initializations, which yields a richer terminal safe set. Furthermore, a new method for selecting states in the terminal set is developed, which keeps the convexity for the terminal safe set and allows for taking suboptimal states.

Airline Crew Pairing Optimization (CPO) aims at generating a set of legal flight sequences (crew pairings), to cover an airline's flight schedule, at minimum cost. It is usually performed using Column Generation (CG), a mathematical programming technique for guided search-space exploration. CG exploits the interdependencies between the current and the preceding CG-iteration for generating new variables (pairings) during the optimization-search. However, with the unprecedented scale and complexity of the emergent flight networks, it has become imperative to learn higher-order interdependencies among the flight-connection graphs, and utilize those to enhance the efficacy of the CPO. In first of its kind and what marks a significant departure from the state-of-the-art, this paper proposes a novel adaptation of the Variational Graph Auto-Encoder for learning plausible combinatorial patterns among the flight-connection data obtained through the search-space exploration by an Airline Crew Pairing Optimizer, AirCROP (developed by the authors and validated by the research consortium's industrial sponsor, GE Aviation). The resulting flight-connection predictions are combined on-the-fly using a novel heuristic to generate new pairings for the optimizer. The utility of the proposed approach is demonstrated on large-scale (over 4200 flights), real-world, complex flight-networks of US-based airlines, characterized by multiple hub-and-spoke subnetworks and several crew bases.

Decision making in real-life scenarios may often be modeled as an optimization problem. It requires the consideration of various attributes like human preferences and thinking, which constrain achieving the optimal value of the problem objectives. The value of the objectives may be maximized or minimized, depending on the situation. Numerous times, the values of these problem parameters are in linguistic form, as human beings naturally understand and express themselves using words. These problems are therefore termed as linguistic optimization problems (LOPs), and are of two types, namely single objective linguistic optimization problems (SOLOPs) and multi-objective linguistic optimization problems (MOLOPs). In these LOPs, the value of the objective function(s) may not be known at all points of the decision space, and therefore, the objective function(s) as well as problem constraints are linked by the if-then rules. Tsukamoto inference method has been used to solve these LOPs; however, it suffers from drawbacks. As, the use of linguistic information inevitably calls for the utilization of computing with words (CWW), and therefore, 2-tuple linguistic model based solution methodologies were proposed for LOPs. However, we found that 2-tuple linguistic model based solution methodologies represent the semantics of the linguistic information using a combination of type-1 fuzzy sets and ordinal term sets. As, the semantics of linguistic information are best modeled using the interval type-2 fuzzy sets, hence we propose solution methodologies for LOPs based on CWW approach of perceptual computing, in this paper. The perceptual computing based solution methodologies use a novel design of CWW engine, called the perceptual reasoning (PR). PR in the current form is suitable for solving SOLOPs and, hence, we have also extended it to the MOLOPs.

This paper presents Semantic SentenceRank (SSR), an unsupervised scheme for automatically ranking sentences in a single document according to their relative importance. In particular, SSR extracts essential words and phrases from a text document, and uses semantic measures to construct, respectively, a semantic phrase graph over phrases and words, and a semantic sentence graph over sentences. It applies two variants of article-structure-biased PageRank to score phrases and words on the first graph and sentences on the second graph. It then combines these scores to generate the final score for each sentence. Finally, SSR solves a multi-objective optimization problem for ranking sentences based on their final scores and topic diversity through semantic subtopic clustering. An implementation of SSR that runs in quadratic time is presented, and it outperforms, on the SummBank benchmarks, each individual judge's ranking and compares favorably with the combined ranking of all judges.

Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an optimum. Recent papers have shown that the optimal search distribution, used for the sampling, might be more peaked around the center of the distribution than the prior distribution modelling our uncertainty about the location of the optimum. We confirm this statement, provide explicit values for this reshaping of the search distribution depending on the population size $\lambda$ and the dimension $d$, and validate our results experimentally.

In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error does not provide sufficient guidance toward desired models. Standard symbolic regression techniques then yield models that are partially incorrect, for instance, in terms of their steady-state characteristics or local behavior. If these properties were considered already during the search process, more accurate and relevant models could be produced. We propose a multi-objective symbolic regression approach that is driven by both the training data and the prior knowledge of the properties the desired model should manifest. The properties given in the form of formal constraints are internally represented by a set of discrete data samples on which candidate models are exactly checked. The proposed approach was experimentally evaluated on three test problems with results clearly demonstrating its capability to evolve realistic models that fit the training data well while complying with the prior knowledge of the desired model characteristics at the same time. It outperforms standard symbolic regression by several orders of magnitude in terms of the mean squared deviation from a reference model.

The concept of free energy has its origins in 19th century thermodynamics, but has recently found its way into the behavioral and neural sciences, where it has been promoted for its wide applicability and has even been suggested as a fundamental principle of understanding intelligent behavior and brain function. We argue that there are essentially two different notions of free energy in current models of intelligent agency, that can both be considered as applications of Bayesian inference to the problem of action selection: one that appears when trading off accuracy and uncertainty based on a general maximum entropy principle, and one that formulates action selection in terms of minimizing an error measure that quantifies deviations of beliefs and policies from given reference models. The first approach provides a normative rule for action selection in the face of model uncertainty or when information-processing capabilities are limited. The second approach directly aims to formulate the action selection problem as an inference problem in the context of Bayesian brain theories, also known as Active Inference in the literature. We elucidate the main ideas and discuss critical technical and conceptual issues revolving around these two notions of free energy that both claim to apply at all levels of decision-making, from the high-level deliberation of reasoning down to the low-level information-processing of perception.

Counterfactual reasoning from logged data has become increasingly important for a large range of applications such as web advertising or healthcare. In this paper, we address the problem of counterfactual risk minimization for learning a stochastic policy with a continuous action space. Whereas previous works have mostly focused on deriving statistical estimators with importance sampling, we show that the optimization perspective is equally important for solving the resulting nonconvex optimization problems.Specifically, we demonstrate the benefits of proximal point algorithms and soft-clipping estimators which are more amenable to gradient-based optimization than classical hard clipping. We propose multiple synthetic, yet realistic, evaluation setups, and we release a new large-scale dataset based on web advertising data for this problem that is crucially missing public benchmarks.