Combinatorial Network Optimization with Unknown Variables: Multi-Armed Bandits with Linear Rewards

In the classic multi-armed bandits problem, the goal is to have a policy for dynamically operating arms that each yield stochastic rewards with unknown means. The key metric of interest is regret, defined as the gap between the expected total reward accumulated by an omniscient player that knows the reward means for each arm, and the expected total reward accumulated by the given policy. The policies presented in prior work have storage, computation and regret all growing linearly with the number of arms, which is not scalable when the number of arms is large. We consider in this work a broad class of multi-armed bandits with dependent arms that yield rewards as a linear combination of a set of unknown parameters. For this general framework, we present efficient policies that are shown to achieve regret that grows logarithmically with time, and polynomially in the number of unknown parameters (even though the number of dependent arms may grow exponentially). Furthermore, these policies only require storage that grows linearly in the number of unknown parameters. We show that this generalization is broadly applicable and useful for many interesting tasks in networks that can be formulated as tractable combinatorial optimization problems with linear objective functions, such as maximum weight matching, shortest path, and minimum spanning tree computations

A Packet Dropping Mechanism for Efficient Operation of M/M/1 Queues with Selfish Users

We consider a fundamental game theoretic problem concerning selfish users contributing packets to an M/M/1 queue. In this game, each user controls its own input rate so as to optimize a desired tradeoff between throughput and delay. We first show that the original game has an inefficient Nash Equilibrium (NE), with a Price of Anarchy (PoA) that scales linearly or worse in the number of users. In order to improve the outcome efficiency, we propose an easily implementable mechanism design whereby the server randomly drops packets with a probability that is a function of the total arrival rate. We show that this results in a modified M/M/1 queueing game that is an ordinal potential game with at least one NE. In particular, for a linear packet dropping function, which is similar to the Random Early Detection (RED) algorithm used in Internet Congestion Control, we prove that there is a unique NE. We also show that the simple best response dynamic converges to this unique equilibrium. Finally, for this scheme, we prove that the social welfare (expressed either as the summation of utilities of all players, or as the summation of the logarithm of utilities of all players) at the equilibrium point can be arbitrarily close to the social welfare at the global optimal point, i.e. the PoA can be made arbitrarily close to 1. We also study the impact of arrival rate estimation error on the PoA through simulations.Comment: This work is an extended version of the conference paper: Y. Gai, H. Liu and B. Krishnamachari, "A packet dropping-based incentive mechanism for M/M/1 queues with selfish users", the 30th IEEE International Conference on Computer Communications (IEEE INFOCOM 2011), China, April, 201

Beyond the space of painting and poetry: Mallarmé and the embodied gesture

Painting cannot be bound by definition; painting’s entanglement with art history, theory, and philosophy is a game of conjecture leading to a proliferation of terms as colourful and singular as a brush mark. This research re-evaluates the terms of painting in the ‘expanded-field’. Rosalind Krauss considers the expanded-field the domain of post-modernism, equating it with ‘the post-medium condition’ – opposing Clement Greenberg’s modernist aesthetic which limits painting to the conventions of its ‘proper medium’. Today the expanded-field opens onto digital space – David Joselit imagines painting as a network, Isabel Graw proposes a ‘residual-specificity’ embedded in a ‘medium-unspecific’ concept of painting. This research re-imagines the space of painting through the space of poetry: through a network of reciprocal relations manifest in Stéphane Mallarmé’s poem Un coup de Dés jamais n’abolira le Hasard, (A throw of the Dice will never abolish Chance). The striking innovation of Mallarmé’s generative poem lies in its capacity for multiple and simultaneous readings, signified in a weaving of word, image, and sound, which Mallarmé presents as a constellation. Through a close reading of Un coup de Dés I suggest a new critical space for painting, demonstrated in Mallarmé’s spatial poetics. I propose that the poem marks the transition from a Modernist ‘absorptive’ mode of looking/reading to a postmodern performative mode, and that Mallarmé is crucial to understanding the relation between content and form. I demonstrate Mallarmé’s relevance to articulating a reductive tendency in painting through a re–appraisal of the structural and spatial organisation of the text, the grid, blank page, and the subsequent sculptural turn that led to a re-negotiation of the space between the object and viewer. Through performative strategies I engage with the text, drawing attention to the metaphoric possibilities of the space of the page and of the book; these include painting, sculpture, video, digital media, installation, and mathematics. Through a formal investigation of line, space, and gesture, painting is presented as a language with its own syntax. My artwork shows that what animates this relation is the embodiment of gesture, as a movement towards the idea perceived, and that the viewer’s relation to the object is negotiated as a gap or a virtual space where meaning constantly unfolds. The distinction between practice and theory, between academic writing and writing as practice, breaks down; research, conceived as a series of dialogues with Mallarmé, re-frames and re-articulates Un coup de Dés. Visual and textual forms are woven together, establishing a direct relation between literature and the plastic arts. This research makes a contribution to Mallarméan studies, and to current discourses relating to painting in the expanded-field, through a re-evaluation of the relation between the space of painting and poetry, and discourses that underpin spatial and temporal readings of the text. I demonstrate the importance of Mallarmé to trans-disciplinary research; extant material from one field applied to another generates new forms embodied in this gesture

Growth diagram and magnetic properties of hexagonal LuFe2_2O4_4 thin films

A growth diagram of Lu-Fe-O compounds on MgO (111) substrates using pulsed laser deposition is constructed based on extensive growth experiments. The LuFe$_2$O$_4$ phase can only be grown in a small range of temperature and O$_2$ pressure conditions. An understanding of the growth mechanism of Lu-Fe-O compound films is offered in terms of the thermochemistry at the surface. Superparamagnetism is observed in LuFe$_2$O$_4$ film and is explained in terms of the effect of the impurity h-LuFeO$_3$ phase and structural defects