36,547 research outputs found
When Can Limited Randomness Be Used in Repeated Games?
The central result of classical game theory states that every finite normal
form game has a Nash equilibrium, provided that players are allowed to use
randomized (mixed) strategies. However, in practice, humans are known to be bad
at generating random-like sequences, and true random bits may be unavailable.
Even if the players have access to enough random bits for a single instance of
the game their randomness might be insufficient if the game is played many
times.
In this work, we ask whether randomness is necessary for equilibria to exist
in finitely repeated games. We show that for a large class of games containing
arbitrary two-player zero-sum games, approximate Nash equilibria of the
-stage repeated version of the game exist if and only if both players have
random bits. In contrast, we show that there exists a class of
games for which no equilibrium exists in pure strategies, yet the -stage
repeated version of the game has an exact Nash equilibrium in which each player
uses only a constant number of random bits.
When the players are assumed to be computationally bounded, if cryptographic
pseudorandom generators (or, equivalently, one-way functions) exist, then the
players can base their strategies on "random-like" sequences derived from only
a small number of truly random bits. We show that, in contrast, in repeated
two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then
random bits remain necessary for equilibria to exist
Comparing knowledge sources for nominal anaphora resolution
We compare two ways of obtaining lexical knowledge for antecedent selection in other-anaphora
and definite noun phrase coreference. Specifically, we compare an algorithm that relies on links
encoded in the manually created lexical hierarchy WordNet and an algorithm that mines corpora
by means of shallow lexico-semantic patterns. As corpora we use the British National
Corpus (BNC), as well as the Web, which has not been previously used for this task. Our
results show that (a) the knowledge encoded in WordNet is often insufficient, especially for
anaphor-antecedent relations that exploit subjective or context-dependent knowledge; (b) for
other-anaphora, the Web-based method outperforms the WordNet-based method; (c) for definite
NP coreference, the Web-based method yields results comparable to those obtained using
WordNet over the whole dataset and outperforms the WordNet-based method on subsets of the
dataset; (d) in both case studies, the BNC-based method is worse than the other methods because
of data sparseness. Thus, in our studies, the Web-based method alleviated the lexical knowledge
gap often encountered in anaphora resolution, and handled examples with context-dependent relations
between anaphor and antecedent. Because it is inexpensive and needs no hand-modelling
of lexical knowledge, it is a promising knowledge source to integrate in anaphora resolution systems
Object-oriented Neural Programming (OONP) for Document Understanding
We propose Object-oriented Neural Programming (OONP), a framework for
semantically parsing documents in specific domains. Basically, OONP reads a
document and parses it into a predesigned object-oriented data structure
(referred to as ontology in this paper) that reflects the domain-specific
semantics of the document. An OONP parser models semantic parsing as a decision
process: a neural net-based Reader sequentially goes through the document, and
during the process it builds and updates an intermediate ontology to summarize
its partial understanding of the text it covers. OONP supports a rich family of
operations (both symbolic and differentiable) for composing the ontology, and a
big variety of forms (both symbolic and differentiable) for representing the
state and the document. An OONP parser can be trained with supervision of
different forms and strength, including supervised learning (SL) ,
reinforcement learning (RL) and hybrid of the two. Our experiments on both
synthetic and real-world document parsing tasks have shown that OONP can learn
to handle fairly complicated ontology with training data of modest sizes.Comment: accepted by ACL 201
Dictionary matching in a stream
We consider the problem of dictionary matching in a stream. Given a set of
strings, known as a dictionary, and a stream of characters arriving one at a
time, the task is to report each time some string in our dictionary occurs in
the stream. We present a randomised algorithm which takes O(log log(k + m))
time per arriving character and uses O(k log m) words of space, where k is the
number of strings in the dictionary and m is the length of the longest string
in the dictionary
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