684 research outputs found
Simulating Noisy Channel Interaction
We show that rounds of interaction over the binary symmetric channel
with feedback can be simulated with
rounds of interaction over a noiseless channel. We also introduce a more
general "energy cost" model of interaction over a noisy channel. We show energy
cost to be equivalent to external information complexity, which implies that
our simulation results are unlikely to carry over to energy complexity. Our
main technical innovation is a self-reduction from simulating a noisy channel
to simulating a slightly-less-noisy channel, which may have other applications
in the area of interactive compression
On Simultaneous Two-player Combinatorial Auctions
We consider the following communication problem: Alice and Bob each have some
valuation functions and over subsets of items,
and their goal is to partition the items into in a way that
maximizes the welfare, . We study both the allocation
problem, which asks for a welfare-maximizing partition and the decision
problem, which asks whether or not there exists a partition guaranteeing
certain welfare, for binary XOS valuations. For interactive protocols with
communication, a tight 3/4-approximation is known for both
[Fei06,DS06].
For interactive protocols, the allocation problem is provably harder than the
decision problem: any solution to the allocation problem implies a solution to
the decision problem with one additional round and additional bits of
communication via a trivial reduction. Surprisingly, the allocation problem is
provably easier for simultaneous protocols. Specifically, we show:
1) There exists a simultaneous, randomized protocol with polynomial
communication that selects a partition whose expected welfare is at least
of the optimum. This matches the guarantee of the best interactive, randomized
protocol with polynomial communication.
2) For all , any simultaneous, randomized protocol that
decides whether the welfare of the optimal partition is or correctly with probability requires
exponential communication. This provides a separation between the attainable
approximation guarantees via interactive () versus simultaneous () protocols with polynomial communication.
In other words, this trivial reduction from decision to allocation problems
provably requires the extra round of communication
Incentivizing Exploration with Selective Data Disclosure
We study the design of rating systems that incentivize (more) efficient
social learning among self-interested agents. Agents arrive sequentially and
are presented with a set of possible actions, each of which yields a positive
reward with an unknown probability. A disclosure policy sends messages about
the rewards of previously-chosen actions to arriving agents. These messages can
alter agents' incentives towards exploration, taking potentially sub-optimal
actions for the sake of learning more about their rewards. Prior work achieves
much progress with disclosure policies that merely recommend an action to each
user, but relies heavily on standard, yet very strong rationality assumptions.
We study a particular class of disclosure policies that use messages, called
unbiased subhistories, consisting of the actions and rewards from a subsequence
of past agents. Each subsequence is chosen ahead of time, according to a
predetermined partial order on the rounds. We posit a flexible model of
frequentist agent response, which we argue is plausible for this class of
"order-based" disclosure policies. We measure the success of a policy by its
regret, i.e., the difference, over all rounds, between the expected reward of
the best action and the reward induced by the policy. A disclosure policy that
reveals full history in each round risks inducing herding behavior among the
agents, and typically has regret linear in the time horizon . Our main
result is an order-based disclosure policy that obtains regret
. This regret is known to be optimal in the worst case
over reward distributions, even absent incentives. We also exhibit simpler
order-based policies with higher, but still sublinear, regret. These policies
can be interpreted as dividing a sublinear number of agents into constant-sized
focus groups, whose histories are then revealed to future agents
Selling to a No-Regret Buyer
We consider the problem of a single seller repeatedly selling a single item
to a single buyer (specifically, the buyer has a value drawn fresh from known
distribution in every round). Prior work assumes that the buyer is fully
rational and will perfectly reason about how their bids today affect the
seller's decisions tomorrow. In this work we initiate a different direction:
the buyer simply runs a no-regret learning algorithm over possible bids. We
provide a fairly complete characterization of optimal auctions for the seller
in this domain. Specifically:
- If the buyer bids according to EXP3 (or any "mean-based" learning
algorithm), then the seller can extract expected revenue arbitrarily close to
the expected welfare. This auction is independent of the buyer's valuation ,
but somewhat unnatural as it is sometimes in the buyer's interest to overbid. -
There exists a learning algorithm such that if the buyer bids
according to then the optimal strategy for the seller is simply
to post the Myerson reserve for every round. - If the buyer bids according
to EXP3 (or any "mean-based" learning algorithm), but the seller is restricted
to "natural" auction formats where overbidding is dominated (e.g. Generalized
First-Price or Generalized Second-Price), then the optimal strategy for the
seller is a pay-your-bid format with decreasing reserves over time. Moreover,
the seller's optimal achievable revenue is characterized by a linear program,
and can be unboundedly better than the best truthful auction yet simultaneously
unboundedly worse than the expected welfare
Coding for interactive communication correcting insertions and deletions
We consider the question of interactive communication, in which two remote
parties perform a computation while their communication channel is
(adversarially) noisy. We extend here the discussion into a more general and
stronger class of noise, namely, we allow the channel to perform insertions and
deletions of symbols. These types of errors may bring the parties "out of
sync", so that there is no consensus regarding the current round of the
protocol.
In this more general noise model, we obtain the first interactive coding
scheme that has a constant rate and resists noise rates of up to
. To this end we develop a novel primitive we name edit
distance tree code. The edit distance tree code is designed to replace the
Hamming distance constraints in Schulman's tree codes (STOC 93), with a
stronger edit distance requirement. However, the straightforward generalization
of tree codes to edit distance does not seem to yield a primitive that suffices
for communication in the presence of synchronization problems. Giving the
"right" definition of edit distance tree codes is a main conceptual
contribution of this work
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