39 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
A constant factor approximation for Nash social welfare with subadditive valuations
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
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
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: proving existence when the number of agents is small, 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 -EFX allocation with charity by establishing a connection to aproblem in extremal combinatorics. We improve their result and prove theexistence of -EFX allocations with 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
For any , we give a simple, deterministic
-approximation algorithm for the Nash social welfare (NSW)
problem under submodular valuations. The previous best approximation factor was
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 -approximation if
the ratio between the largest weight and the average weight is at most
.
We also show that the -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 -EFX and a
-approximation to the symmetric NSW problem under submodular
valuations. The previous best approximation factor under -EFX was linear
in the number of agents.Comment: 28 pages, 1 figur
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
Excursions at the Interface of Topological Phases of Matter and Quantum Error Correction
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
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Essays on Online Learning and Resource Allocation
This thesis studies four independent resource allocation problems with different assumptions on information available to the central planner, and strategic considerations of the agents present in the system.
We start off with an online, non-strategic agents setting in Chapter 1, where we study the dynamic pricing and learning problem under the Bass demand model. The main objective in the field of dynamic pricing and learning is to study how a seller can maximize revenue by adjusting price over time based on sequentially realized demand. Unlike most existing literature on dynamic pricing and learning, where the price only affects the demand in the current period, under the Bass model, price also influences the future evolution of demand. Finding arevenue-maximizing dynamic pricing policy in this model is non-trivial even in the full information case, where model parameters are known. We consider the more challenging incomplete information problem where dynamic pricing is applied in conjunction with learning the unknown model parameters, with the objective of optimizing the cumulative revenues over a given selling horizon of length . Our main contribution is an algorithm that satisfies a high probability regret guarantee of order ²/³; where the market size is known a priori. Moreover, we show that no algorithm can incur smaller order of loss by deriving a matching lower bound.
We then switch our attention to a single round, strategic agents setting in Chapter 2, where we study a multi-resource allocation problem with heterogeneous demands and Leontief utilities. Leontief utility function captures the idea that for certain resource allocation settings, the utility of marginal increase in one resource depends on the availabilities of other resources. We generalize the existing literature on this model formulation to incorporate more constraints faced in real applications, which in turn requires new algorithm design and analysis techniques. The main contribution of this chapter is an allocation algorithm that satisfies Pareto optimality, envy-freenss, strategy-proofness, and a notion of sharing incentive.
In Chapter 3, we study a single round, non-strategic agent setting, where the central planner tries to allocate a pool of items to a set of agents who each has to receive a prespecified fraction of all items. Additionally, we want to ensure fairness by controlling the amount of envy that agents have with the final allocations. We make the observation that this resource allocation setting can be formulated as an Optimal Transport problem, and that the solution structure displays a surprisingly simple structure. Using this insight, we are able to design an allocation algorithm that achieves the optimal trade-off between efficiency and envy.
Finally, in Chapter 4 we study an online, strategic agent setting, where similar to the previous chapter, the central planner needs to allocate a pool of items to a set of agents who each has to receive a prespecified fraction of all items. Unlike in the previous chapter, the central planner has no a priori information on the distribution of items. Instead, the central planner needs to implicitly learn these distributions from the observed values in order to pick a good allocation policy. Additionally, an added challenge here is that the agents are strategic with incentives to misreport their valuations in order to receive better allocations. This sets our work apart both from the online auction mechanism design settings which typically assume known valuation distributions and/or involve payments, and from the online learning settings that do not consider strategic agents. To that end, our main contribution is an online learning based allocation mechanism that is approximately Bayesian incentive compatible, and when all agents are truthful, guarantees a sublinear regret for individual agents' utility compared to that under the optimal offline allocation policy
Expanding Task Diversity in Explanation-Based Interactive Task Learning
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