亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

We introduce the Conic Blackwell Algorithm$^+$ (CBA$^+$) regret minimizer, a new parameter- and scale-free regret minimizer for general convex sets. CBA$^+$ is based on Blackwell approachability and attains $O(\sqrt{T})$ regret. We show how to efficiently instantiate CBA$^+$ for many decision sets of interest, including the simplex, $\ell_{p}$ norm balls, and ellipsoidal confidence regions in the simplex. Based on CBA$^+$, we introduce SP-CBA$^+$, a new parameter-free algorithm for solving convex-concave saddle-point problems, which achieves a $O(1/\sqrt{T})$ ergodic rate of convergence. In our simulations, we demonstrate the wide applicability of SP-CBA$^+$ on several standard saddle-point problems, including matrix games, extensive-form games, distributionally robust logistic regression, and Markov decision processes. In each setting, SP-CBA$^+$ achieves state-of-the-art numerical performance, and outperforms classical methods, without the need for any choice of step sizes or other algorithmic parameters.

We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of the Stochastic Mirror Descent algorithm with a particular class of uniformly convex mirror maps, in terms of the number of iterations, dimensionality and related geometric parameters of the optimization problem. Interestingly this algorithm does not require any explicit gradient clipping or normalization, which have been extensively used in several recent empirical and theoretical works. We complement our convergence results with information-theoretic lower bounds showing that no other algorithm using only stochastic first-order oracles can achieve improved rates. Our results have several interesting consequences for devising online/streaming stochastic approximation algorithms for problems arising in robust statistics and machine learning.

We introduce the "inverse bandit" problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement learning assume the execution of an optimal policy, and thereby suffer from an identifiability issue. In contrast, we propose to leverage the demonstrator's behavior en route to optimality, and in particular, the exploration phase, for reward estimation. We begin by establishing a general information-theoretic lower bound under this paradigm that applies to any demonstrator algorithm, which characterizes a fundamental tradeoff between reward estimation and the amount of exploration of the demonstrator. Then, we develop simple and efficient reward estimators for upper-confidence-based demonstrator algorithms that attain the optimal tradeoff, showing in particular that consistent reward estimation -- free of identifiability issues -- is possible under our paradigm. Extensive simulations on both synthetic and semi-synthetic data corroborate our theoretical results.

Bisimulation metrics define a distance measure between states of a Markov decision process (MDP) based on a comparison of reward sequences. Due to this property they provide theoretical guarantees in value function approximation. In this work we first prove that bisimulation metrics can be defined via any $p$-Wasserstein metric for $p\geq 1$. Then we describe an approximate policy iteration (API) procedure that uses $\epsilon$-aggregation with $\pi$-bisimulation and prove performance bounds for continuous state spaces. We bound the difference between $\pi$-bisimulation metrics in terms of the change in the policies themselves. Based on these theoretical results, we design an API($\alpha$) procedure that employs conservative policy updates and enjoys better performance bounds than the naive API approach. In addition, we propose a novel trust region approach which circumvents the requirement to explicitly solve a constrained optimization problem. Finally, we provide experimental evidence of improved stability compared to non-conservative alternatives in simulated continuous control.

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to guarantee both optimism and convergence of the associated value iteration scheme. We prove that EB-SSP achieves the minimax regret rate $\widetilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the number of episodes, $S$ is the number of states, $A$ is the number of actions and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of $B_{\star}$, nor of $T_{\star}$ which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of $T_{\star}$ is available) where the regret only contains a logarithmic dependence on $T_{\star}$, thus yielding the first horizon-free regret bound beyond the finite-horizon MDP setting.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

Proximal Policy Optimization (PPO) is a highly popular model-free reinforcement learning (RL) approach. However, in continuous state and actions spaces and a Gaussian policy -- common in computer animation and robotics -- PPO is prone to getting stuck in local optima. In this paper, we observe a tendency of PPO to prematurely shrink the exploration variance, which naturally leads to slow progress. Motivated by this, we borrow ideas from CMA-ES, a black-box optimization method designed for intelligent adaptive Gaussian exploration, to derive PPO-CMA, a novel proximal policy optimization approach that can expand the exploration variance on objective function slopes and shrink the variance when close to the optimum. This is implemented by using separate neural networks for policy mean and variance and training the mean and variance in separate passes. Our experiments demonstrate a clear improvement over vanilla PPO in many difficult OpenAI Gym MuJoCo tasks.

We consider the exploration-exploitation trade-off in reinforcement learning and we show that an agent imbued with a risk-seeking utility function is able to explore efficiently, as measured by regret. The parameter that controls how risk-seeking the agent is can be optimized exactly, or annealed according to a schedule. We call the resulting algorithm K-learning and show that the corresponding K-values are optimistic for the expected Q-values at each state-action pair. The K-values induce a natural Boltzmann exploration policy for which the `temperature' parameter is equal to the risk-seeking parameter. This policy achieves an expected regret bound of $\tilde O(L^{3/2} \sqrt{S A T})$, where $L$ is the time horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the total number of elapsed time-steps. This bound is only a factor of $L$ larger than the established lower bound. K-learning can be interpreted as mirror descent in the policy space, and it is similar to other well-known methods in the literature, including Q-learning, soft-Q-learning, and maximum entropy policy gradient, and is closely related to optimism and count based exploration methods. K-learning is simple to implement, as it only requires adding a bonus to the reward at each state-action and then solving a Bellman equation. We conclude with a numerical example demonstrating that K-learning is competitive with other state-of-the-art algorithms in practice.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.

This work considers the problem of provably optimal reinforcement learning for episodic finite horizon MDPs, i.e. how an agent learns to maximize his/her long term reward in an uncertain environment. The main contribution is in providing a novel algorithm --- Variance-reduced Upper Confidence Q-learning (vUCQ) --- which enjoys a regret bound of $\widetilde{O}(\sqrt{HSAT} + H^5SA)$, where the $T$ is the number of time steps the agent acts in the MDP, $S$ is the number of states, $A$ is the number of actions, and $H$ is the (episodic) horizon time. This is the first regret bound that is both sub-linear in the model size and asymptotically optimal. The algorithm is sub-linear in that the time to achieve $\epsilon$-average regret for any constant $\epsilon$ is $O(SA)$, which is a number of samples that is far less than that required to learn any non-trivial estimate of the transition model (the transition model is specified by $O(S^2A)$ parameters). The importance of sub-linear algorithms is largely the motivation for algorithms such as $Q$-learning and other "model free" approaches. vUCQ algorithm also enjoys minimax optimal regret in the long run, matching the $\Omega(\sqrt{HSAT})$ lower bound. Variance-reduced Upper Confidence Q-learning (vUCQ) is a successive refinement method in which the algorithm reduces the variance in $Q$-value estimates and couples this estimation scheme with an upper confidence based algorithm. Technically, the coupling of both of these techniques is what leads to the algorithm enjoying both the sub-linear regret property and the asymptotically optimal regret.