308 research outputs found
Stable Principal Component Pursuit
In this paper, we study the problem of recovering a low-rank matrix (the
principal components) from a high-dimensional data matrix despite both small
entry-wise noise and gross sparse errors. Recently, it has been shown that a
convex program, named Principal Component Pursuit (PCP), can recover the
low-rank matrix when the data matrix is corrupted by gross sparse errors. We
further prove that the solution to a related convex program (a relaxed PCP)
gives an estimate of the low-rank matrix that is simultaneously stable to small
entrywise noise and robust to gross sparse errors. More precisely, our result
shows that the proposed convex program recovers the low-rank matrix even though
a positive fraction of its entries are arbitrarily corrupted, with an error
bound proportional to the noise level. We present simulation results to support
our result and demonstrate that the new convex program accurately recovers the
principal components (the low-rank matrix) under quite broad conditions. To our
knowledge, this is the first result that shows the classical Principal
Component Analysis (PCA), optimal for small i.i.d. noise, can be made robust to
gross sparse errors; or the first that shows the newly proposed PCP can be made
stable to small entry-wise perturbations.Comment: 5-page paper submitted to ISIT 201
Vanishing of black hole tidal Love numbers from scattering amplitudes
We extract the black hole (BH) static tidal deformability coefficients (Love
numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes
for fields to scatter off a spinning BH in the worldline effective field theory
(EFT) and in general relativity (GR). We point out that the GR amplitudes due
to tidal effects originate entirely from the BH potential region. Thus, they
can be separated from gravitational non-linearities in the wave region, whose
proper treatment requires higher order EFT loop calculations. In particular,
the elastic scattering in the near field approximation is produced exclusively
by tidal effects. We find this contribution to vanish identically, which
implies that the static Love numbers of Kerr BHs are zero for all types of
perturbations. We also reproduce the known behavior of scalar Love numbers for
higher dimensional BHs. Our results are manifestly gauge-invariant and
coordinate-independent, thereby providing a valuable consistency check for the
commonly used off-shell methods.Comment: 7 pages, 1 figure, comments are welcom
A Cost-effective Shuffling Method against DDoS Attacks using Moving Target Defense
Moving Target Defense (MTD) has emerged as a newcomer into the asymmetric
field of attack and defense, and shuffling-based MTD has been regarded as one
of the most effective ways to mitigate DDoS attacks. However, previous work
does not acknowledge that frequent shuffles would significantly intensify the
overhead. MTD requires a quantitative measure to compare the cost and
effectiveness of available adaptations and explore the best trade-off between
them. In this paper, therefore, we propose a new cost-effective shuffling
method against DDoS attacks using MTD. By exploiting Multi-Objective Markov
Decision Processes to model the interaction between the attacker and the
defender, and designing a cost-effective shuffling algorithm, we study the best
trade-off between the effectiveness and cost of shuffling in a given shuffling
scenario. Finally, simulation and experimentation on an experimental software
defined network (SDN) indicate that our approach imposes an acceptable
shuffling overload and is effective in mitigating DDoS attacks
Model-Free, Regret-Optimal Best Policy Identification in Online CMDPs
This paper considers the best policy identification (BPI) problem in online
Constrained Markov Decision Processes (CMDPs). We are interested in algorithms
that are model-free, have low regret, and identify an optimal policy with a
high probability. Existing model-free algorithms for online CMDPs with
sublinear regret and constraint violation do not provide any convergence
guarantee to an optimal policy and provide only average performance guarantees
when a policy is uniformly sampled at random from all previously used policies.
In this paper, we develop a new algorithm, named
Pruning-Refinement-Identification (PRI), based on a fundamental structural
property of CMDPs proved in Koole(1988); Ross(1989), which we call limited
stochasticity. The property says for a CMDP with constraints, there exists
an optimal policy with at most stochastic decisions.
The proposed algorithm first identifies at which step and in which state a
stochastic decision has to be taken and then fine-tunes the distributions of
these stochastic decisions. PRI achieves trio objectives: (i) PRI is a
model-free algorithm; and (ii) it outputs a near-optimal policy with a high
probability at the end of learning; and (iii) in the tabular setting, PRI
guarantees regret and constraint violation,
which significantly improves the best existing regret bound
under a model-free algorithm, where
is the total number of episodes
Sharp Variance-Dependent Bounds in Reinforcement Learning: Best of Both Worlds in Stochastic and Deterministic Environments
We study variance-dependent regret bounds for Markov decision processes
(MDPs). Algorithms with variance-dependent regret guarantees can automatically
exploit environments with low variance (e.g., enjoying constant regret on
deterministic MDPs). The existing algorithms are either variance-independent or
suboptimal. We first propose two new environment norms to characterize the
fine-grained variance properties of the environment. For model-based methods,
we design a variant of the MVP algorithm (Zhang et al., 2021a) and use new
analysis techniques show to this algorithm enjoys variance-dependent bounds
with respect to our proposed norms. In particular, this bound is simultaneously
minimax optimal for both stochastic and deterministic MDPs, the first result of
its kind. We further initiate the study on model-free algorithms with
variance-dependent regret bounds by designing a reference-function-based
algorithm with a novel capped-doubling reference update schedule. Lastly, we
also provide lower bounds to complement our upper bounds.Comment: ICML 202
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