279 research outputs found
A Puzzle about Further Facts
In metaphysics, there are a number of distinct but related questions about
the existence of "further facts" -- facts that are contingent relative to the
physical structure of the universe. These include further facts about qualia,
personal identity, and time. In this article I provide a sequence of examples
involving computer simulations, ranging from one in which the protagonist can
clearly conclude such further facts exist to one that describes our own
condition. This raises the question of where along the sequence (if at all) the
protagonist stops being able to soundly conclude that further facts exist.Comment: To appear in Erkenntnis: An International Journal of Scientific
Philosoph
Universal Voting Protocol Tweaks to Make Manipulation Hard
Voting is a general method for preference aggregation in multiagent settings,
but seminal results have shown that all (nondictatorial) voting protocols are
manipulable. One could try to avoid manipulation by using voting protocols
where determining a beneficial manipulation is hard computationally. A number
of recent papers study the complexity of manipulating existing protocols. This
paper is the first work to take the next step of designing new protocols that
are especially hard to manipulate. Rather than designing these new protocols
from scratch, we instead show how to tweak existing protocols to make
manipulation hard, while leaving much of the original nature of the protocol
intact. The tweak studied consists of adding one elimination preround to the
election. Surprisingly, this extremely simple and universal tweak makes typical
protocols hard to manipulate! The protocols become NP-hard, #P-hard, or
PSPACE-hard to manipulate, depending on whether the schedule of the preround is
determined before the votes are collected, after the votes are collected, or
the scheduling and the vote collecting are interleaved, respectively. We prove
general sufficient conditions on the protocols for this tweak to introduce the
hardness, and show that the most common voting protocols satisfy those
conditions. These are the first results in voting settings where manipulation
is in a higher complexity class than NP (presuming PSPACE NP)
AWESOME: A General Multiagent Learning Algorithm that Converges in Self-Play and Learns a Best Response Against Stationary Opponents
A satisfactory multiagent learning algorithm should, {\em at a minimum},
learn to play optimally against stationary opponents and converge to a Nash
equilibrium in self-play. The algorithm that has come closest, WoLF-IGA, has
been proven to have these two properties in 2-player 2-action repeated
games--assuming that the opponent's (mixed) strategy is observable. In this
paper we present AWESOME, the first algorithm that is guaranteed to have these
two properties in {\em all} repeated (finite) games. It requires only that the
other players' actual actions (not their strategies) can be observed at each
step. It also learns to play optimally against opponents that {\em eventually
become} stationary. The basic idea behind AWESOME ({\em Adapt When Everybody is
Stationary, Otherwise Move to Equilibrium}) is to try to adapt to the others'
strategies when they appear stationary, but otherwise to retreat to a
precomputed equilibrium strategy. The techniques used to prove the properties
of AWESOME are fundamentally different from those used for previous algorithms,
and may help in analyzing other multiagent learning algorithms also
BL-WoLF: A Framework For Loss-Bounded Learnability In Zero-Sum Games
We present BL-WoLF, a framework for learnability in repeated zero-sum games
where the cost of learning is measured by the losses the learning agent accrues
(rather than the number of rounds). The game is adversarially chosen from some
family that the learner knows. The opponent knows the game and the learner's
learning strategy. The learner tries to either not accrue losses, or to quickly
learn about the game so as to avoid future losses (this is consistent with the
Win or Learn Fast (WoLF) principle; BL stands for ``bounded loss''). Our
framework allows for both probabilistic and approximate learning. The resultant
notion of {\em BL-WoLF}-learnability can be applied to any class of games, and
allows us to measure the inherent disadvantage to a player that does not know
which game in the class it is in. We present {\em guaranteed
BL-WoLF-learnability} results for families of games with deterministic payoffs
and families of games with stochastic payoffs. We demonstrate that these
families are {\em guaranteed approximately BL-WoLF-learnable} with lower cost.
We then demonstrate families of games (both stochastic and deterministic) that
are not guaranteed BL-WoLF-learnable. We show that those families,
nevertheless, are {\em BL-WoLF-learnable}. To prove these results, we use a key
lemma which we derive
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