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# AI

## Finite-Sample Convergence Rates for Q-Learning and Indirect Algorithms

Finite-Sample Convergence Rates for Q-Learning and Indirect Algorithms finite-sample convergence rates for q-learning and indirect algorithms

## Solving H-horizon, Stationary Markov Decision Problems In Time Proportional To Log(H)

Solving H-horizon, Stationary Markov Decision Problems In Time Proportional To Log(H) Solving h-horizon, stationary markov decision problems in time proportional to log (h) Paul Tseng, Operations Reseserch Letters 9 (1990) 287-297.

## Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Run Time

Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Run Time Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Run Time The nonlinear Bellman equation =  linear programming problem: Primal-Dual LP Primal LP (1) Dual LP (2)   Minmax Problem (3)

## KL Divergence

KL Divergence In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy) is a measure of how one probability distribution is different from a second, reference probability distribution. https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence Information entropy KL Divergence

## The Asymptotic Convergence-Rate of Q-learning

The Asymptotic Convergence-Rate of Q-learning the-asymptotic-convergence-rate-of-q-learning The asymptotic rate of convergence of Q-learning is Ο( 1/tR(1-γ) ), if R(1-γ)<0.5, where R=Pmin/Pmax, P is state-action occupation frequency. |Qt (x,a) − Q*(x,a)| < B/tR(1-γ) Convergence-rate is the difference between True value and Optimum value, i.e., the smaller it is, the faster convergence Q-learning is. We hope the Ο( 1/tR(1-γ) ) should… read more »

## Hierarchical Apprenticeship Learning, with Application to Quadruped Locomotion

Hierarchical Apprenticeship Learning, with Application to Quadruped Locomotion   本论文关键在于机器狗走路经过崎岖路面到达goal的特殊性决定了比较方便选low-level：四条腿，与地面接触，high-level：整体重心，与goal直线距离（关于专家建议）。后面有分析。 图5表明机器狗的足迹，学习前和学习后差别很大，只用footstep约束（四条腿）会使机器狗走弯路，我理解是四条腿更关心路面的崎岖程度，哪里更不容易卡住或者摔倒就走哪里，而body path planner计划机器狗重心近似轨迹（在terrain上方）到goal，可以理解成path更关心到goal的直线距离。 机器狗在测试terrain中只从path-level demonstration过不去，也就是说如果只关心机器狗重心到goal的直线距离而不关心4条腿与地面接触就不能到达goal，因为机器狗会在路面上摔倒或者卡住。

Policy Gradient Methods In summary, I guess because 1. policy (probability of action) has the style: , 2. obtain (or let’s say ‘math trick’) in the objective function ( i.e., value function )’s gradient equation to get an ‘Expectation’ form for : , assign ‘ln’ to policy before gradient for analysis convenience. pg Notation J(θ):… read more »

## Actor-Critic Algorithms for Hierarchical Markov Decision Processes

Actor-Critic Algorithms for Hierarchical Markov Decision Processes

## Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation

Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation 当环境给的奖励少而延迟时，论文给出了一个解决方案：agent至始至终只有一个，但分两个阶段：1总控器阶段，选goal，2控制器，根据当前state和goal，输出action，critic判断goal是否完成或达到终态。重复1,2。总控器选一个新的goal，控制器再输出action，依次类推。我理解它把环境“分”出N个时序上的小环境，与每个小环境对应1个goal。agent实体在这种环境下可以等效为一个点。 The key is that the policy over goals πg which makes expected Q-value with discounting maximum is the policy which the agent chooses, i.e., if the goal sequence g1-g3-g2-… ‘s Q-value is the maximum value among that of all kinds of goal sequences, the agent should… read more »

## Meta Learning Shared Hierarchies

Meta Learning Shared Hierarchies Notation S: state space. A: action space. MDP: transition function P(s’, r|s, a), (s’, r): next state and reward, (s,a): state and action. PM : distribution over MDPs M with the same state-action space (S, A). Agent: a function mapping from a multi-episode history (s0, a0, r0, s1, a2, r2, …… read more »

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