11,734 research outputs found
Last Round Convergence and No-Instant Regret in Repeated Games with Asymmetric Information
This paper considers repeated games in which one player has more information
about the game than the other players. In particular, we investigate repeated
two-player zero-sum games where only the column player knows the payoff matrix
A of the game. Suppose that while repeatedly playing this game, the row player
chooses her strategy at each round by using a no-regret algorithm to minimize
her (pseudo) regret. We develop a no-instant-regret algorithm for the column
player to exhibit last round convergence to a minimax equilibrium. We show that
our algorithm is efficient against a large set of popular no-regret algorithms
of the row player, including the multiplicative weight update algorithm, the
online mirror descent method/follow-the-regularized-leader, the linear
multiplicative weight update algorithm, and the optimistic multiplicative
weight update
Exploiting No-Regret Algorithms in System Design
We investigate a repeated two-player zero-sum game setting where the column
player is also a designer of the system, and has full control on the design of
the payoff matrix. In addition, the row player uses a no-regret algorithm to
efficiently learn how to adapt their strategy to the column player's behaviour
over time in order to achieve good total payoff. The goal of the column player
is to guide her opponent to pick a mixed strategy which is favourable for the
system designer. Therefore, she needs to: (i) design an appropriate payoff
matrix whose unique minimax solution contains the desired mixed strategy of
the row player; and (ii) strategically interact with the row player during a
sequence of plays in order to guide her opponent to converge to that desired
behaviour. To design such a payoff matrix, we propose a novel solution that
provably has a unique minimax solution with the desired behaviour. We also
investigate a relaxation of this problem where uniqueness is not required, but
all the minimax solutions have the same mixed strategy for the row player.
Finally, we propose a new game playing algorithm for the system designer and
prove that it can guide the row player, who may play a \emph{stable} no-regret
algorithm, to converge to a minimax solution
On the Asymptotic Capacity of -Secure -Private Information Retrieval with Graph Based Replicated Storage
The problem of private information retrieval with graph-based replicated
storage was recently introduced by Raviv, Tamo and Yaakobi. Its capacity
remains open in almost all cases. In this work the asymptotic (large number of
messages) capacity of this problem is studied along with its generalizations to
include arbitrary -privacy and -security constraints, where the privacy
of the user must be protected against any set of up to colluding servers
and the security of the stored data must be protected against any set of up to
colluding servers. A general achievable scheme for arbitrary storage
patterns is presented that achieves the rate , where
is the total number of servers, and each message is replicated at least
times. Notably, the scheme makes use of a special structure
inspired by dual Generalized Reed Solomon (GRS) codes. A general converse is
also presented. The two bounds are shown to match for many settings, including
symmetric storage patterns. Finally, the asymptotic capacity is fully
characterized for the case without security constraints for arbitrary
storage patterns provided that each message is replicated no more than
times. As an example of this result, consider PIR with arbitrary graph based
storage () where every message is replicated at exactly servers.
For this -replicated storage setting, the asymptotic capacity is equal to
where is the maximum size of a -matching in a
storage graph . In this undirected graph, the vertices correspond
to the set of servers, and there is an edge between vertices
only if a subset of messages is replicated at both servers and
A Tight Algorithm for Strongly Connected Steiner Subgraph On Two Terminals With Demands
Given an edge-weighted directed graph on vertices and a set
of terminals, the objective of the \scss
(-SCSS) problem is to find an edge set of minimum weight such
that contains an path for each . In this paper, we investigate the computational complexity of a variant of
-SCSS where we have demands for the number of paths between each terminal
pair. Formally, the \sharinggeneral problem is defined as follows: given an
edge-weighted directed graph with weight function , two terminal vertices , and integers
; the objective is to find a set of paths from and paths from
such that is minimized,
where . For each , we show the following: The \sharing problem
can be solved in time. A matching lower bound for our algorithm: the
\sharing problem does not have an algorithm for any
computable function , unless the Exponential Time Hypothesis (ETH) fails.
Our algorithm for \sharing relies on a structural result regarding an optimal
solution followed by using the idea of a "token game" similar to that of
Feldman and Ruhl. We show with an example that the structural result does not
hold for the \sharinggeneral problem if . Therefore
\sharing is the most general problem one can attempt to solve with our
techniques.Comment: To appear in Algorithmica. An extended abstract appeared in IPEC '1
Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories
Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by â. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation
A match coefficient approach for damage imaging in structural components by ultrasonic synthetic aperture focus
Ultrasonic Synthetic Aperture Focus (SAF) techniques are commonly used to image structural defects. In this paper, a variation of SAF based on ideas borrowed from Matched Field Processing (MFP) is evaluated to reduce artifacts and sidelobes of the resulting images. In particular, instead of considering the full RF ultrasonic waveforms for the SAF time backpropagation, only selected features from the waveforms are utilized to form a âdata vectorâ and a âreplicaâ (expected) vector of MFP. These vectors are adaptive for the pair of transmitter-receiver and the focus point. The image is created as a matched filter between these two vectors. Experimental results are shown for an isotropic and homogenous metallic plate with simulated defects, probed by six piezoelectric patches used as receivers or transmitters
Non-supersymmetric heterotic model building
We investigate orbifold and smooth Calabi-Yau compactifications of the
non-supersymmetric heterotic SO(16)xSO(16) string. We focus on such Calabi-Yau
backgrounds in order to recycle commonly employed techniques, like index
theorems and cohomology theory, to determine both the fermionic and bosonic 4D
spectra. We argue that the N=0 theory never leads to tachyons on smooth
Calabi-Yaus in the large volume approximation. As twisted tachyons may arise on
certain singular orbifolds, we conjecture that such tachyonic states are lifted
in the full blow-up. We perform model searches on selected orbifold geometries.
In particular, we construct an explicit example of a Standard Model-like theory
with three generations and a single Higgs field.Comment: 1+30 pages latex, 11 tables; v2: references and minor revisions
added, matches version published in JHE
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