75 research outputs found
Consensus Propagation
We propose consensus propagation, an asynchronous distributed protocol for
averaging numbers across a network. We establish convergence, characterize the
convergence rate for regular graphs, and demonstrate that the protocol exhibits
better scaling properties than pairwise averaging, an alternative that has
received much recent attention. Consensus propagation can be viewed as a
special case of belief propagation, and our results contribute to the belief
propagation literature. In particular, beyond singly-connected graphs, there
are very few classes of relevant problems for which belief propagation is known
to converge.Comment: journal versio
On the Flow-level Dynamics of a Packet-switched Network
The packet is the fundamental unit of transportation in modern communication
networks such as the Internet. Physical layer scheduling decisions are made at
the level of packets, and packet-level models with exogenous arrival processes
have long been employed to study network performance, as well as design
scheduling policies that more efficiently utilize network resources. On the
other hand, a user of the network is more concerned with end-to-end bandwidth,
which is allocated through congestion control policies such as TCP.
Utility-based flow-level models have played an important role in understanding
congestion control protocols. In summary, these two classes of models have
provided separate insights for flow-level and packet-level dynamics of a
network
Optimal Dynamic Fees for Blockchain Resources
We develop a general and practical framework to address the problem of the
optimal design of dynamic fee mechanisms for multiple blockchain resources. Our
framework allows to compute policies that optimally trade-off between adjusting
resource prices to handle persistent demand shifts versus being robust to local
noise in the observed block demand. In the general case with more than one
resource, our optimal policies correctly handle cross-effects (complementarity
and substitutability) in resource demands. We also show how these cross-effects
can be used to inform resource design, i.e. combining resources into bundles
that have low demand-side cross-effects can yield simpler and more efficient
price-update rules. Our framework is also practical, we demonstrate how it can
be used to refine or inform the design of heuristic fee update rules such as
EIP-1559 or EIP-4844 with two case studies. We then estimate a uni-dimensional
version of our model using real market data from the Ethereum blockchain and
empirically compare the performance of our optimal policies to EIP-1559
Approximate Dynamic Programming via a Smoothed Linear Program
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural “projection” of a well-studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program—the “smoothed approximate linear program”—is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. These bounds are, in general, no worse than those available for extant LP approaches and for specific problem instances can be shown to be arbitrarily stronger. Second, experiments with our approach on a pair of challenging problems (the game of Tetris and a queueing network control problem) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several ADP algorithms) by a substantial margin
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