Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (IA), also known as iterated deletion of weakly dominated strategies, where uncertainty is represented using LPSs (lexicographic probability sequences). Their characterization holds in a rich structure called a complete structure, where all types are possible. In earlier work, we gave a characterization of iterated admissibility using an "all I know" operator, that captures the intuition that "all the agent knows" is that agents satisfy the appropriate rationality assumptions. That characterization did not need complete structures and used probability structures, not LPSs. However, that characterization did not deal with Samuelson's conceptual concern regarding IA, namely, that at higher levels, players do not consider possible strategies that were used to justify their choice of strategy at lower levels. In this paper, we give a characterization of IA using the all I know operator that does deal with Samuelson's concern. However, it uses LPSs. We then show how to modify the characterization using notions of "approximate belief" and "approximately all I know" so as to deal with Samuelson's concern while still working with probability structures.

Gossip protocols are programs used in a setting in which each agent holds a secret and the aim is to reach a situation in which all agents know all secrets. Such protocols rely on a point-to-point or group communication. Distributed epistemic gossip protocols use epistemic formulas in the component programs for the agents. The advantage of the use of epistemic logic is that the resulting protocols are very concise and amenable for a simple verification. Recently, we introduced a natural modal logic that allows one to express distributed epistemic gossip protocols and to reason about their correctness. We proved that the resulting protocols are implementable and that all aspects of their correctness, including termination, are decidable. To establish these results we showed that both the definition of semantics and of truth of the underlying logic are decidable. We also showed that the analogous results hold for an extension of this logic with the 'common knowledge' operator. However, several, often deceptively simple, questions about this logic and the corresponding gossip protocols remain open. The purpose of this paper is to list and elucidate these questions and provide for them an appropriate background information in the form of partial of related results.

The recent success of Deep Neural Networks (DNNs) has revealed the significant capability of neuromorphic computing in many challenging applications. Although DNNs are derived from emulating biological neurons, there still exist doubts over whether or not DNNs are the final and best model to emulate the mechanism of human intelligence. In particular, there are two discrepancies between computational DNN models and the observed facts of biological neurons. First, human neurons are interconnected randomly, while DNNs need carefully-designed architectures to work properly. Second, human neurons usually have a long spiking latency (~100ms) which implies that not many layers can be involved in making a decision, while DNNs could have hundreds of layers to guarantee high accuracy. In this paper, we propose a new computational neuromorphic model, namely shallow unorganized neural networks (SUNNs), in contrast to DNNs. The proposed SUNNs differ from standard ANNs or DNNs in three fundamental aspects: 1) SUNNs are based on an adaptive neuron cell model, Smart Neurons, that allows each neuron to adaptively respond to its inputs rather than carrying out a fixed weighted-sum operation like the neuron model in ANNs/DNNs; 2) SUNNs cope with computational tasks using only shallow architectures; 3) SUNNs have a natural topology with random interconnections, as the human brain does, and as proposed by Turing's B-type unorganized machines. We implemented the proposed SUNN architecture and tested it on a number of unsupervised early stage visual perception tasks. Surprisingly, such shallow architectures achieved very good results in our experiments. The success of our new computational model makes it a working example of Turing's B-Type machine that can achieve comparable or better performance against the state-of-the-art algorithms.

A collection of $U \: (\in \mathbb{N})$ data vectors is called a $U$-tuple, and the association strength among the vectors of a tuple is termed as the hyperlink weight, that is assumed to be symmetric with respect to permutation of the entries in the index. We herein propose Bregman hyperlink regression (BHLR), which learns a user-specified symmetric similarity function such that it predicts the tuple's hyperlink weight from data vectors stored in the $U$-tuple. Nonlinear functions, such as neural networks, can be employed for the similarity function. BHLR is based on Bregman divergence (BD) and encompasses various existing methods such as logistic regression ($U=1$), Poisson regression ($U=1$), graph embedding ($U=2$), matrix factorization ($U=2$), tensor factorization ($U \geq 2$), and their variants equipped with arbitrary BD. We demonstrate that, regardless of the choice of BD and $U \in \mathbb{N}$, the proposed BHLR is generally (P-1) robust against the distributional misspecification, that is, it asymptotically recovers the underlying true conditional expectation of hyperlink weights given data vectors regardless of its conditional distribution, and (P-2) computationally tractable, that is, it is efficiently computed by stochastic optimization algorithms using a novel generalized minibatch sampling procedure for hyper-relational data. Furthermore, a theoretical guarantee for the optimization is presented. Numerical experiments demonstrate the promising performance of the proposed BHLR.

Action detection and recognition tasks have been the target of much focus in the computer vision community due to their many applications, namely, security, robotics and recommendation systems. Recently, datasets like AVA, provide multi-person, multi-label, spatiotemporal action detection and recognition challenges. Being unable to discern which portions of the input to use for classification is a limitation of two-stream CNN approaches, once the vision task involves several people with several labels. We address this limitation and improve the state-of-the-art performance of two-stream CNNs. In this paper we present four contributions: our fovea attention filtering that highlights targets for classification without discarding background; a generalized binary loss function designed for the AVA dataset; miniAVA, a partition of AVA that maintains temporal continuity and class distribution with only one tenth of the dataset size; and ablation studies on alternative attention filters. Our method, using fovea attention filtering and our generalized binary loss, achieves a relative video mAP improvement of 20% over the two-stream baseline in AVA, and is competitive with the state-of-the-art in the UCF101-24. We also show a relative video mAP improvement of 12.6% when using our generalized binary loss over the standard sum-of-sigmoids.

In multi-agent path finding (MAPF) the task is to navigate agents from their starting positions to given individual goals. The problem takes place in an undirected graph whose vertices represent positions and edges define the topology. Agents can move to neighbor vertices across edges. In the standard MAPF, space occupation by agents is modeled by a capacity constraint that permits at most one agent per vertex. We suggest an extension of MAPF in this paper that permits more than one agent per vertex. Propositional satisfiability (SAT) models for these extensions of MAPF are studied. We focus on modeling capacity constraints in SAT-based formulations of MAPF and evaluation of performance of these models. We extend two existing SAT-based formulations with vertex capacity constraints: MDD-SAT and SMT-CBS where the former is an approach that builds the model in an eager way while the latter relies on lazy construction of the model.

Knowledge can be represented compactly in multiple ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a database modelled as a first-order relational structure. In the presence of integrity constraints, we identify classes of aggregators that respect them in the aggregated database, provided these are satisfied in all individual databases. We also characterise languages for first-order queries on which the answer to a query on the aggregated database coincides with the aggregation of the answers to the query obtained on each individual database. This contribution is meant to be a first step on the application of techniques from social choice theory to knowledge representation in databases.

We propose a new model for forming beliefs and learning about unknown probabilities (such as the probability of picking a red marble from a bag with an unknown distribution of coloured marbles). The most widespread model for such situations of 'radical uncertainty' is in terms of imprecise probabilities, i.e. representing the agent's knowledge as a set of probability measures. We add to this model a plausibility map, associating to each measure a plausibility number, as a way to go beyond what is known with certainty and represent the agent's beliefs about probability. There are a number of standard examples: Shannon Entropy, Centre of Mass etc. We then consider learning of two types of information: (1) learning by repeated sampling from the unknown distribution (e.g. picking marbles from the bag); and (2) learning higher-order information about the distribution (in the shape of linear inequalities, e.g. we are told there are more red marbles than green marbles). The first changes only the plausibility map (via a 'plausibilistic' version of Bayes' Rule), but leaves the given set of measures unchanged; the second shrinks the set of measures, without changing their plausibility. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. But our belief change does not comply with standard AGM axioms, since the revision induced by (1) is of a non-AGM type. This is essential, as it allows our agents to learn the true probability: we prove that the beliefs obtained by repeated sampling converge almost surely to the correct belief (in the true probability). We end by sketching the contours of a dynamic doxastic logic for statistical learning.

This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a finite set of explicitly given scenarios. It is shown that both problem variants are NPhard. To solve the consid ered variants, several heuristics based on local search or evolutionar y computing are proposed. The heuristics are experimentally evaluated on appr opriate problem instances.

In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex) regularization function. The proposed algorithm incorporates ideas from several existing approaches such as alternate direction method of multipliers (ADMM), successive convex approximation (SCA), distributed and asynchronous algorithms, and inexact gradient methods. Different from a number of existing approaches, however, the proposed framework is flexible enough to incorporate a class of non-convex objective functions, allow distributed operation with and without a fusion center, and include variance reduced methods as special cases. Remarkably, the proposed algorithms are robust to uncertainties arising from random, deterministic, and adversarial sources. The part I of the paper develops two variants of the algorithm under very mild assumptions and establishes first-order convergence rate guarantees. The proof developed here allows for generic errors and delays, paving the way for different variance-reduced, asynchronous, and stochastic implementations, outlined and evaluated in part II.