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Large-scale statistical machine learning

Title
Large-scale statistical machine learning
Funding
ARC | Australian Laureate Fellowships
Contract (GA) number
FL110100281
Start Date
2011/01/01
End Date
2016/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/FL110100281

 

  • Robustness of Bayesian Pool-based Active Learning Against Prior Misspecification

    Cuong, Nguyen Viet; Ye, Nan; Lee, Wee Sun (2016)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all $\alpha$-approximate algorithms are robust (i.e., near $\alpha$-approximate) if the utility is Lipschitz continuous in the prior. We further show that robustness may not be achieved if the utility is non-Lips...

    Best of both worlds: Stochastic & adversarial best-arm identification

    Abbasi-Yadkori , Yasin; Bartlett , Peter; Gabillon , Victor; Malek , Alan; Valko , Michal (2018)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    International audience; We study bandit best-arm identification with arbitrary and potentially adversarial rewards. A simple random uniform learner obtains the optimal rate of error in the adversarial scenario. However, this type of strategy is suboptimal when the rewards are sampled stochastically. Therefore, we ask: Can we design a learner that performs optimally in both the stochastic and adversarial problems while not being aware of the nature of the rewards? First, we show that designing...

    Best of both worlds: Stochastic & adversarial best-arm identification

    Abbasi-Yadkori , Yasin; Bartlett , Peter; Gabillon , Victor; Malek , Alan; Valko , Michal (2018)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    International audience; We study bandit best-arm identification with arbitrary and potentially adversarial rewards. A simple random uniform learner obtains the optimal rate of error in the adversarial scenario. However, this type of strategy is suboptimal when the rewards are sampled stochastically. Therefore, we ask: Can we design a learner that performs optimally in both the stochastic and adversarial problems while not being aware of the nature of the rewards? First, we show that designing...

    #Exploration: A Study of Count-Based Exploration for Deep Reinforcement Learning

    Tang, Haoran; Houthooft, Rein; Foote, Davis; Stooke, Adam; Chen, Xi; Duan, Yan; Schulman, John; De Turck, Filip; Abbeel, Pieter (2016)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    Count-based exploration algorithms are known to perform near-optimally when used in conjunction with tabular reinforcement learning (RL) methods for solving small discrete Markov decision processes (MDPs). It is generally thought that count-based methods cannot be applied in high-dimensional state spaces, since most states will only occur once. Recent deep RL exploration strategies are able to deal with high-dimensional continuous state spaces through complex heuristics, often relying on opti...

    Acceleration and Averaging in Stochastic Mirror Descent Dynamics

    Krichene, Walid; Bartlett, Peter L. (2017)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a stochastic variant in which the gradient is contaminated by noise, and study the resulting stochastic differential equation. We prove a bound on the rate of change of an energy function associated with the problem, then use it to derive estimates of convergence rate...

    Representing smooth functions as compositions of near-identity functions with implications for deep network optimization

    Bartlett, Peter L.; Evans, Steven N.; Long, Philip M. (2018)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    We show that any smooth bi-Lipschitz $h$ can be represented exactly as a composition $h_m \circ ... \circ h_1$ of functions $h_1,...,h_m$ that are close to the identity in the sense that each $\left(h_i-\mathrm{Id}\right)$ is Lipschitz, and the Lipschitz constant decreases inversely with the number $m$ of functions composed. This implies that $h$ can be represented to any accuracy by a deep residual network whose nonlinear layers compute functions with a small Lipschitz constant. Next, we con...

    Alternating minimization for dictionary learning with random initialization

    Chatterji, Niladri S.; Bartlett, Peter L. (2017)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate basis (dictionary) $A^*$ and sparse vectors $x^{1*},\ldots,x^{n*}$. Our algorithm is a simple alternating minimization procedure that switches between $\ell_1$ minimization and gradient descent in alternate steps. Dictionary learning and specifically alternat...

    Gradient descent with identity initialization efficiently learns positive definite linear transformations by deep residual networks

    Bartlett, Peter L.; Helmbold, David P.; Long, Philip M. (2018)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    We analyze algorithms for approximating a function $f(x) = \Phi x$ mapping $\Re^d$ to $\Re^d$ using deep linear neural networks, i.e. that learn a function $h$ parameterized by matrices $\Theta_1,...,\Theta_L$ and defined by $h(x) = \Theta_L \Theta_{L-1} ... \Theta_1 x$. We focus on algorithms that learn through gradient descent on the population quadratic loss in the case that the distribution over the inputs is isotropic. We provide polynomial bounds on the number of iterations for gradient...

    Online learning with kernel losses

    Pacchiano, Aldo; Chatterji, Niladri S.; Bartlett, Peter L. (2018)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the exponential weights algorithm and bound its regret in this setting. Under conditions on the eigendecay of the kernel we provide a sharp characterization of the regret for this algorithm. When we have polynomial eigendecay $\mu_j \le \mathcal{O}(j^{-\beta})$, we fin...

    RL$^2$: Fast Reinforcement Learning via Slow Reinforcement Learning

    Duan, Yan; Schulman, John; Chen, Xi; Bartlett, Peter L.; Sutskever, Ilya; Abbeel, Pieter (2016)
    Projects: ARC | Large-scale statistical machine learning (FL110100281)
    Deep reinforcement learning (deep RL) has been successful in learning sophisticated behaviors automatically; however, the learning process requires a huge number of trials. In contrast, animals can learn new tasks in just a few trials, benefiting from their prior knowledge about the world. This paper seeks to bridge this gap. Rather than designing a "fast" reinforcement learning algorithm, we propose to represent it as a recurrent neural network (RNN) and learn it from data. In our proposed m...
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