39 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    A constant factor approximation for Nash social welfare with subadditive valuations

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    We present a constant-factor approximation algorithm for the Nash social welfare maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a template for NSW optimization by solving a configuration-type LP and using a rounding procedure for (utilitarian) social welfare as a blackbox, which could be applicable to other variants of the problem

    Understanding Quantum Technologies 2022

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    Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma

    EFX Allocations: Simplifications and Improvements

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    The existence of EFX allocations is a fundamental open problem in discretefair division. Given a set of agents and indivisible goods, the goal is todetermine the existence of an allocation where no agent envies anotherfollowing the removal of any single good from the other agent's bundle. Sincethe general problem has been illusive, progress is made on two fronts: (i)(i)proving existence when the number of agents is small, (ii)(ii) proving existenceof relaxations of EFX. In this paper, we improve results on both fronts (andsimplify in one of the cases). We prove the existence of EFX allocations with three agents, restricting onlyone agent to have an MMS-feasible valuation function (a strict generalizationof nice-cancelable valuation functions introduced by Berger et al. whichsubsumes additive, budget-additive and unit demand valuation functions). Theother agents may have any monotone valuation functions. Our proof technique issignificantly simpler and shorter than the proof by Chaudhury et al. onexistence of EFX allocations when there are three agents with additivevaluation functions and therefore more accessible. Secondly, we consider relaxations of EFX allocations, namely, approximate-EFXallocations and EFX allocations with few unallocated goods (charity). Chaudhuryet al. showed the existence of (1−ϵ)(1-\epsilon)-EFX allocation withO((n/ϵ)45)O((n/\epsilon)^{\frac{4}{5}}) charity by establishing a connection to aproblem in extremal combinatorics. We improve their result and prove theexistence of (1−ϵ)(1-\epsilon)-EFX allocations with O~((n/ϵ)12)\tilde{O}((n/\epsilon)^{\frac{1}{2}}) charity. In fact, some of our techniques can be usedto prove improved upper-bounds on a problem in zero-sum combinatoricsintroduced by Alon and Krivelevich.<br

    Approximating Nash Social Welfare by Matching and Local Search

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    For any ε>0\varepsilon>0, we give a simple, deterministic (6+ε)(6+\varepsilon)-approximation algorithm for the Nash social welfare (NSW) problem under submodular valuations. The previous best approximation factor was 380380 via a randomized algorithm. We also consider the asymmetric variant of the problem, where the objective is to maximize the weighted geometric mean of agents' valuations, and give an (ω+2+ε)e(\omega + 2 +\varepsilon) e-approximation if the ratio between the largest weight and the average weight is at most ω\omega. We also show that the 1/21/2-EFX envy-freeness property can be attained simultaneously with a constant-factor approximation. More precisely, we can find an allocation in polynomial time which is both 1/21/2-EFX and a (12+ε)(12+\varepsilon)-approximation to the symmetric NSW problem under submodular valuations. The previous best approximation factor under 1/21/2-EFX was linear in the number of agents.Comment: 28 pages, 1 figur

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    Excursions at the Interface of Topological Phases of Matter and Quantum Error Correction

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    Topological quantum error-correcting codes are a family of stabilizer codes that are built using a lattice of qubits covering some manifold. The stabilizers of the code are local with respect to the underlying lattice, and logical information is encoded in the non-local degrees of freedom. The locality of stabilizers in these codes makes them especially suitable for experiments. From the condensed matter perspective, their code space corresponds to the ground state subspace of a local Hamiltonian belonging to a non-trivial topological phase of matter. The stabilizers of the code correspond to the Hamiltonian terms, and errors can be thought of as excitations above the ground state subspace. Conversely, one can use fixed point Hamiltonian of a topological phase of matter to define a topological quantum error-correcting code.This close connection has motivated numerous studies which utilize insights from one view- point to address questions in the other. This thesis further explores the possibilities in this di- rection. In the first two chapters, we present novel schemes to implement logical gates, which are motivated by viewing topological quantum error-correcting codes as topological phases of matter. In the third chapter, we show how the quantum error correction perspective could be used to realize robust topological entanglement phases in monitored random quantum circuits. And in the last chapter, we explore the possibility of extending this connection beyond topological quan- tum error-correcting codes. In particular, we introduce an order parameter for detecting k-local non-trivial states, which can be thought of as a generalization of topological states that includes codewords of any quantum error-correcting code

    Expanding Task Diversity in Explanation-Based Interactive Task Learning

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    The possibility of having artificial agents that can interact with humans and learn completely new tasks through instruction and demonstration is an exciting prospect. This is the goal of the emerging research area of Interactive Task Learning. Solving this problem requires integrating many capabilities across AI to create general robot learns that can operate in a variety of environments. One particular challenge is that the space of possible tasks is extremely large and varied. Developing approaches that cover this space is a difficult challenge, made more so by having to learn from a limited, though high-quality, number of examples given through interaction with a teacher. In this dissertation, we identify three major dimensions of task complexity (diverse types of actions, task formulations, and task modifiers), and describe extensions that demonstrate greater learning capabilities for each dimension than previous work. First, we extend the representations and learning mechanism for innate tasks so the agent can learn tasks that utilize many different types of actions beyond physical object manipulation, such as communication and mental operations. Second, we implement a novel goal-graph representation that supports both goal-based and procedural tasks. Thus the instructor can formulate a task as achieving a goal and let the agent use planning to execute it, or can formulate the task as executing a procedure, or sequence of steps, when it is not easy to define a goal. This also allows interesting cases of a task that blends elements of a procedure and goal. Third, we added support for learning subtasks with various modifying clauses, such as temporal constraints, conditions, or looping structures. Crucially, we show that the agent can learn and generalize a canonical version of a task and then combine it with these various modifiers within a task hierarchy without requiring additional instruction. This is done in the context of Rosie -- an agent implemented within the Soar cognitive architecture that can learn completely new tasks in one shot through situated interactive instruction. By leveraging explanation-based generalization and domain knowledge, the agent quickly learns new hierarchical tasks, including their structure, arguments, goals, execution policies, and task decompositions, through natural language instruction. It has been used with various robotic platforms, though most of the learning demonstrations and evaluations in this work use a simulated mobile robot in a multi-room, partially-observable environment. In the end, we show that the agent can combine all of these extensions while learning complex hierarchical tasks that cover extended periods of time and demonstrate significant flexibility.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168026/1/mininger_1.pd
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