1,094,860 research outputs found
Constrained Monotone Function Maximization and the Supermodular Degree
The problem of maximizing a constrained monotone set function has many
practical applications and generalizes many combinatorial problems.
Unfortunately, it is generally not possible to maximize a monotone set function
up to an acceptable approximation ratio, even subject to simple constraints.
One highly studied approach to cope with this hardness is to restrict the set
function. An outstanding disadvantage of imposing such a restriction on the set
function is that no result is implied for set functions deviating from the
restriction, even slightly. A more flexible approach, studied by Feige and
Izsak, is to design an approximation algorithm whose approximation ratio
depends on the complexity of the instance, as measured by some complexity
measure. Specifically, they introduced a complexity measure called supermodular
degree, measuring deviation from submodularity, and designed an algorithm for
the welfare maximization problem with an approximation ratio that depends on
this measure.
In this work, we give the first (to the best of our knowledge) algorithm for
maximizing an arbitrary monotone set function, subject to a k-extendible
system. This class of constraints captures, for example, the intersection of
k-matroids (note that a single matroid constraint is sufficient to capture the
welfare maximization problem). Our approximation ratio deteriorates gracefully
with the complexity of the set function and k. Our work can be seen as
generalizing both the classic result of Fisher, Nemhauser and Wolsey, for
maximizing a submodular set function subject to a k-extendible system, and the
result of Feige and Izsak for the welfare maximization problem. Moreover, when
our algorithm is applied to each one of these simpler cases, it obtains the
same approximation ratio as of the respective original work.Comment: 23 page
A Standalone FPGA-based Miner for Lyra2REv2 Cryptocurrencies
Lyra2REv2 is a hashing algorithm that consists of a chain of individual
hashing algorithms, and it is used as a proof-of-work function in several
cryptocurrencies. The most crucial and exotic hashing algorithm in the
Lyra2REv2 chain is a specific instance of the general Lyra2 algorithm. This
work presents the first hardware implementation of the specific instance of
Lyra2 that is used in Lyra2REv2. Several properties of the aforementioned
algorithm are exploited in order to optimize the design. In addition, an
FPGA-based hardware implementation of a standalone miner for Lyra2REv2 on a
Xilinx Multi-Processor System on Chip is presented. The proposed Lyra2REv2
miner is shown to be significantly more energy efficient than both a GPU and a
commercially available FPGA-based miner. Finally, we also explain how the
simplified Lyra2 and Lyra2REv2 architectures can be modified with minimal
effort to also support the recent Lyra2REv3 chained hashing algorithm.Comment: 13 pages, accepted for publication in IEEE Trans. Circuits Syst. I.
arXiv admin note: substantial text overlap with arXiv:1807.0576
Meta Inverse Reinforcement Learning via Maximum Reward Sharing for Human Motion Analysis
This work handles the inverse reinforcement learning (IRL) problem where only
a small number of demonstrations are available from a demonstrator for each
high-dimensional task, insufficient to estimate an accurate reward function.
Observing that each demonstrator has an inherent reward for each state and the
task-specific behaviors mainly depend on a small number of key states, we
propose a meta IRL algorithm that first models the reward function for each
task as a distribution conditioned on a baseline reward function shared by all
tasks and dependent only on the demonstrator, and then finds the most likely
reward function in the distribution that explains the task-specific behaviors.
We test the method in a simulated environment on path planning tasks with
limited demonstrations, and show that the accuracy of the learned reward
function is significantly improved. We also apply the method to analyze the
motion of a patient under rehabilitation.Comment: arXiv admin note: text overlap with arXiv:1707.0939
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