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Reinforcement learning (RL) problems over general state and action spaces are notoriously challenging. In contrast to the tableau setting, one can not enumerate all the states and then iteratively update the policies for each state. This prevents the application of many well-studied RL methods especially those with provable convergence guarantees. In this paper, we first present a substantial generalization of the recently developed policy mirror descent method to deal with general state and action spaces. We introduce new approaches to incorporate function approximation into this method, so that we do not need to use explicit policy parameterization at all. Moreover, we present a novel policy dual averaging method for which possibly simpler function approximation techniques can be applied. We establish linear convergence rate to global optimality or sublinear convergence to stationarity for these methods applied to solve different classes of RL problems under exact policy evaluation. We then define proper notions of the approximation errors for policy evaluation and investigate their impact on the convergence of these methods applied to general-state RL problems with either finite-action or continuous-action spaces. To the best of our knowledge, the development of these algorithmic frameworks as well as their convergence analysis appear to be new in the literature.

In this paper we present new arithmetical and algebraic results following the work of Babindamana and al. on hyperbolas and describe in the new results an approach to attacking a RSA-type modulus based on continued fractions, independent and not bounded by the size of the private key $d$ nor the public exponent $e$ compared to Wiener's attack. When successful, this attack is bounded by $\displaystyle\mathcal{O}\left( b\log{\alpha_{j4}}\log{(\alpha_{i3}+\alpha_{j3})}\right)$ with $b=10^{y}$, $\alpha_{i3}+\alpha_{j3}$ a non trivial factor of $n$ and $\alpha_{j4}$ such that $(n+1)/(n-1)=\alpha_{i4}/\alpha_{j4}$. The primary goal of this attack is to find a point $\displaystyle X_{\alpha}=\left(-\alpha_{3}, \ \alpha_{3}+1 \right) \in \mathbb{Z}^{2}_{\star}$ that satisfies $\displaystyle\left\langle X_{\alpha_{3}}, \ P_{3} \right\rangle =0$ from a convergent of $\displaystyle\frac{\alpha_{i4}}{\alpha_{j4}}+\delta$, with $P_{3}\in \mathcal{B}_{n}(x, y)_{\mid_{x\geq 4n}}$. We finally present some experimental examples. We believe these results constitute a new direction in RSA Cryptanalysis using continued fractions independently of parameters $e$ and $d$.

Federated learning (FL) is a prospective distributed machine learning framework that can preserve data privacy. In particular, cross-silo FL can complete model training by making isolated data islands of different organizations collaborate with a parameter server (PS) via exchanging model parameters for multiple communication rounds. In cross-silo FL, an incentive mechanism is indispensable for motivating data owners to contribute their models to FL training. However, how to allocate the reward budget among different rounds is an essential but complicated problem largely overlooked by existing works. The challenge of this problem lies in the opaque feedback between reward budget allocation and model utility improvement of FL, making the optimal reward budget allocation complicated. To address this problem, we design an online reward budget allocation algorithm using Bayesian optimization named BARA (\underline{B}udget \underline{A}llocation for \underline{R}everse \underline{A}uction). Specifically, BARA can model the complicated relationship between reward budget allocation and final model accuracy in FL based on historical training records so that the reward budget allocated to each communication round is dynamically optimized so as to maximize the final model utility. We further incorporate the BARA algorithm into reverse auction-based incentive mechanisms to illustrate its effectiveness. Extensive experiments are conducted on real datasets to demonstrate that BARA significantly outperforms competitive baselines by improving model utility with the same amount of reward budget.

Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function $f(x,y)$, where $x$ is given to Alice and $y$ is given to Bob, and only one message from Alice to Bob is allowed. A fundamental question in quantum information is the relationship between one-way quantum and classical communication complexities, i.e., how much shorter the message can be if Alice is sending a quantum state instead of bit strings? We make some progress towards this question with the following results. Let $f: \mathcal{X} \times \mathcal{Y} \rightarrow \mathcal{Z} \cup \{\bot\}$ be a partial function and $\mu$ be a distribution with support contained in $f^{-1}(\mathcal{Z})$. Denote $d=|\mathcal{Z}|$. Let $\mathsf{R}^{1,\mu}_\epsilon(f)$ be the classical one-way communication complexity of $f$; $\mathsf{Q}^{1,\mu}_\epsilon(f)$ be the quantum one-way communication complexity of $f$ and $\mathsf{Q}^{1,\mu, *}_\epsilon(f)$ be the entanglement-assisted quantum one-way communication complexity of $f$, each with distributional error (average error over $\mu$) at most $\epsilon$. We show: 1) If $\mu$ is a product distribution, $\eta > 0$ and $0 \leq \epsilon \leq 1-1/d$, then, $$\mathsf{R}^{1,\mu}_{2\epsilon -d\epsilon^2/(d-1)+ \eta}(f) \leq 2\mathsf{Q}^{1,\mu, *}_{\epsilon}(f) + O(\log\log (1/\eta))\enspace.$$ 2)If $\mu$ is a non-product distribution and $\mathcal{Z}=\{ 0,1\}$, then $\forall \epsilon, \eta > 0$ such that $\epsilon/\eta + \eta < 0.5$, $$\mathsf{R}^{1,\mu}_{3\eta}(f) = O(\mathsf{Q}^{1,\mu}_{{\epsilon}}(f) \cdot \mathsf{CS}(f)/\eta^3)\enspace,$$ where \[\mathsf{CS}(f) = \max_{y} \min_{z\in\{0,1\}} \vert \{x~|~f(x,y)=z\} \vert \enspace.\]

We study fair division of indivisible chores among $n$ agents with additive disutility functions. Two well-studied fairness notions for indivisible items are envy-freeness up to one/any item (EF1/EFX) and the standard notion of economic efficiency is Pareto optimality (PO). There is a noticeable gap between the results known for both EF1 and EFX in the goods and chores settings. The case of chores turns out to be much more challenging. We reduce this gap by providing slightly relaxed versions of the known results on goods for the chores setting. Interestingly, our algorithms run in polynomial time, unlike their analogous versions in the goods setting. We introduce the concept of $k$ surplus which means that up to $k$ more chores are allocated to the agents and each of them is a copy of an original chore. We present a polynomial-time algorithm which gives EF1 and PO allocations with $(n-1)$ surplus. We relax the notion of EFX slightly and define tEFX which requires that the envy from agent $i$ to agent $j$ is removed upon the transfer of any chore from the $i$'s bundle to $j$'s bundle. We give a polynomial-time algorithm that in the chores case for $3$ agents returns an allocation which is either proportional or tEFX. Note that proportionality is a very strong criterion in the case of indivisible items, and hence both notions we guarantee are desirable.

Modern DNN workloads increasingly rely on activation functions consisting of computationally complex operations. This poses a challenge to current accelerators optimized for convolutions and matrix-matrix multiplications. This work presents Flex-SFU, a lightweight hardware accelerator for activation functions implementing non-uniform piecewise interpolation supporting multiple data formats. Non-Uniform segments and floating-point numbers are enabled by implementing a binary-tree comparison within the address decoding unit. An SGD-based optimization algorithm with heuristics is proposed to find the interpolation function reducing the mean squared error. Thanks to non-uniform interpolation and floating-point support, Flex-SFU achieves on average 22.3x better mean squared error compared to previous piecewise linear interpolation approaches. The evaluation with more than 700 computer vision and natural language processing models shows that Flex-SFU can, on average, improve the end-to-end performance of state-of-the-art AI hardware accelerators by 35.7%, achieving up to 3.3x speedup with negligible impact in the models' accuracy when using 32 segments, and only introducing an area and power overhead of 5.9% and 0.8% relative to the baseline vector processing unit.

One of the most important topics in discrete fair division is whether an EFX allocation exists for any instance. Although the existence of EFX allocations is a standing open problem for both goods and chores, the understanding of the existence of EFX allocations for chores is less established compared to goods. We study the existence of EFX allocation for chores under the assumption that all agent's cost functions are additive. Specifically, we show the existence of EFX allocations for the following three cases: (i) the number of chores is at most twice the number of agents, (ii) the cost functions of all agents except for one are identical ordering, and (iii) the number of agents is three and each agent has a personalized bi-valued cost function. Furthermore, we provide a polynomial time algorithm to find an EFX allocation for each case.

Extended Boolean functions (EBFs) are one of the most important tools in cryptography and spreading sequence design in communication systems. In this paper, we use EBFs to design new sets of spreading sequences for non-orthogonal multiple access (NOMA), which is an emerging technique capable of supporting massive machine-type communications (mMTC) in 5G and beyond. In this work, first $p$-ary complementary sequences are constructed using EBFs and then, these sequences are used to design new sets of non-orthogonal spreading sequence sets having very low coherence and peak to average power ratio (PAPR). The proposed spreading sequence sets are capable of supporting a large number of active devices simultaneously. In fact, for a $p$-ary spreading sequence set, we theoretically achieve an overloading factor of $2p$, where $p$ is an odd prime. Specifically, for $p=3$, we achieve an overloading factor of $6$, which cannot be achieved through the existing constructions till date.

We study the fair allocation of mixtures of indivisible goods and chores under lexicographic preferences$\unicode{x2014}$a subdomain of additive preferences. A prominent fairness notion for allocating indivisible items is envy-freeness up to any item (EFX). Yet, its existence and computation has remained a notable open problem. By identifying a class of instances with "terrible chores", we show that determining the existence of an EFX allocation is NP-complete. This result immediately implies the intractability of EFX under additive preferences. Nonetheless, we propose a natural subclass of lexicographic preferences for which an EFX and Pareto optimal (PO) allocation is guaranteed to exist and can be computed efficiently for any mixed instance. Focusing on two weaker fairness notions, we investigate finding EF1 and PO allocations for special instances with terrible chores, and show that MMS and PO allocations can be computed efficiently for any mixed instance with lexicographic preferences.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.