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In this paper we introduce a new approach to discrete-time semi-Markov decision processes based on the sojourn time process. Different characterizations of discrete-time semi-Markov processes are exploited and decision processes are constructed by their means. With this new approach, the agent is allowed to consider different actions depending also on the sojourn time of the process in the current state. A numerical method based on $Q$-learning algorithms for finite horizon reinforcement learning and stochastic recursive relations is investigated. Finally, we consider two toy examples: one in which the reward depends on the sojourn-time, according to the gambler's fallacy; the other in which the environment is semi-Markov even if the reward function does not depend on the sojourn time. These are used to carry on some numerical evaluations on the previously presented $Q$-learning algorithm and on a different naive method based on deep reinforcement learning.

Neural memory enables fast adaptation to new tasks with just a few training samples. Existing memory models store features only from the single last layer, which does not generalize well in presence of a domain shift between training and test distributions. Rather than relying on a flat memory, we propose a hierarchical alternative that stores features at different semantic levels. We introduce a hierarchical prototype model, where each level of the prototype fetches corresponding information from the hierarchical memory. The model is endowed with the ability to flexibly rely on features at different semantic levels if the domain shift circumstances so demand. We meta-learn the model by a newly derived hierarchical variational inference framework, where hierarchical memory and prototypes are jointly optimized. To explore and exploit the importance of different semantic levels, we further propose to learn the weights associated with the prototype at each level in a data-driven way, which enables the model to adaptively choose the most generalizable features. We conduct thorough ablation studies to demonstrate the effectiveness of each component in our model. The new state-of-the-art performance on cross-domain and competitive performance on traditional few-shot classification further substantiates the benefit of hierarchical variational memory.

Specifications of complex, large scale, computer software and hardware systems can be radically simplified by using simple maps from input sequences to output values. These "state machine maps" provide an alternative representation of classical Moore type state machines. Composition of state machine maps corresponds to state machine products and can be used to specify essentially any type of interconnection as well as parallel and distributed computation. State machine maps can also specify abstract properties of systems and are significantly more concise and scalable than traditional representations of automata. Examples included here include specifications of producer/consumer software, network distributed consensus, real-time digital circuits, and operating system scheduling. The motivation for this work comes from experience designing and developing operating systems and real-time software where weak methods for understanding and exploring designs is a well known handicap. The methods introduced here are based on ordinary discrete mathematics, primitive recursive functions and deterministic state machines and are intended, initially, to aid the intuition and understanding of the system developers. Staying strictly within the boundaries of classical deterministic state machines anchors the methods to the algebraic structures of automata and semigroups, obviates any need for axiomatic deduction systems, "formal methods", or extensions to the model, and makes the specifications more faithful to engineering practice. While state machine maps are obvious representations of state machines, the techniques introduced here for defining and composing them are novel.

Reinforcement learning (RL) has shown promise as a tool for engineering safe, ethical, or legal behaviour in autonomous agents. Its use typically relies on assigning punishments to state-action pairs that constitute unsafe or unethical choices. Despite this assignment being a crucial step in this approach, however, there has been limited discussion on generalizing the process of selecting punishments and deciding where to apply them. In this paper, we adopt an approach that leverages an existing framework -- the normative supervisor of (Neufeld et al., 2021) -- during training. This normative supervisor is used to dynamically translate states and the applicable normative system into defeasible deontic logic theories, feed these theories to a theorem prover, and use the conclusions derived to decide whether or not to assign a punishment to the agent. We use multi-objective RL (MORL) to balance the ethical objective of avoiding violations with a non-ethical objective; we will demonstrate that our approach works for a multiplicity of MORL techniques, and show that it is effective regardless of the magnitude of the punishment we assign.

In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that considering a time discretization with a positive step size $h$ an error bound of size $h$ can be proved for the difference between the value function (viscosity solution of the Hamilton-Jacobi-Bellman equation corresponding to the infinite horizon) and the value function of the discrete time problem. However, including also a spatial discretization based on elements of size $k$ an error bound of size $O(k/h)$ can be found in the literature for the error between the value functions of the continuous problem and the fully discrete problem. In this paper we revise the error bound of the fully discrete method and prove, under similar assumptions to those of the time discrete case, that the error of the fully discrete case is in fact $O(h+k)$ which gives first order in time and space for the method. This error bound matches the numerical experiments of many papers in the literature in which the behaviour $1/h$ from the bound $O(k/h)$ have not been observed.

Multi-Agent Systems (MAS) are notoriously complex and hard to verify. In fact, it is not trivial to model a MAS, and even when a model is built, it is not always possible to verify, in a formal way, that it is actually behaving as we expect. Usually, it is relevant to know whether an agent is capable of fulfilling its own goals. One possible way to check this is through Model Checking. Specifically, by verifying Alternating-time Temporal Logic (ATL) properties, where the notion of strategies for achieving goals can be described. Unfortunately, the resulting model checking problem is not decidable in general. In this paper, we present a verification procedure based on combining Model Checking and Runtime Verification, where sub-models of the MAS model belonging to decidable fragments are verified by a model checker, and runtime monitors are used to verify the rest. Furthermore, we implement our technique and show experimental results.

Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of maintaining a MaxIS over dynamic graphs has attracted increasing attention over the past few years. Due to the intractability of maintaining an exact MaxIS, this paper aims to develop efficient algorithms that can maintain an approximate MaxIS with an accuracy guarantee theoretically. In particular, we propose a framework that maintains a $(\frac{\Delta}{2} + 1)$-approximate MaxIS over dynamic graphs and prove that it achieves a constant approximation ratio in many real-world networks. To the best of our knowledge, this is the first non-trivial approximability result for the dynamic MaxIS problem. Following the framework, we implement an efficient linear-time dynamic algorithm and a more effective dynamic algorithm with near-linear expected time complexity. Our thorough experiments over real and synthetic graphs demonstrate the effectiveness and efficiency of the proposed algorithms, especially when the graph is highly dynamic.

Parts represent a basic unit of geometric and semantic similarity across different objects. We argue that part knowledge should be composable beyond the observed object classes. Towards this, we present 3D Compositional Zero-shot Learning as a problem of part generalization from seen to unseen object classes for semantic segmentation. We provide a structured study through benchmarking the task with the proposed Compositional-PartNet dataset. This dataset is created by processing the original PartNet to maximize part overlap across different objects. The existing point cloud part segmentation methods fail to generalize to unseen object classes in this setting. As a solution, we propose DeCompositional Consensus, which combines a part segmentation network with a part scoring network. The key intuition to our approach is that a segmentation mask over some parts should have a consensus with its part scores when each part is taken apart. The two networks reason over different part combinations defined in a per-object part prior to generate the most suitable segmentation mask. We demonstrate that our method allows compositional zero-shot segmentation and generalized zero-shot classification, and establishes the state of the art on both tasks.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Many tasks in natural language processing can be viewed as multi-label classification problems. However, most of the existing models are trained with the standard cross-entropy loss function and use a fixed prediction policy (e.g., a threshold of 0.5) for all the labels, which completely ignores the complexity and dependencies among different labels. In this paper, we propose a meta-learning method to capture these complex label dependencies. More specifically, our method utilizes a meta-learner to jointly learn the training policies and prediction policies for different labels. The training policies are then used to train the classifier with the cross-entropy loss function, and the prediction policies are further implemented for prediction. Experimental results on fine-grained entity typing and text classification demonstrate that our proposed method can obtain more accurate multi-label classification results.