Policy optimization is an effective reinforcement learning approach to solve continuous control tasks. Recent achievements have shown that alternating on-line and off-line optimization is a successful choice for efficient trajectory reuse. However, deciding when to stop optimizing and collect new trajectories is non-trivial as it requires to account for the variance of the objective function estimate. In this paper, we propose a novel model-free policy search algorithm, POIS, applicable in both control-based and parameter-based settings. We first derive a high-confidence bound for importance sampling estimation and then we define a surrogate objective function which is optimized off-line using a batch of trajectories. Finally, the algorithm is tested on a selection of continuous control tasks, with both linear and deep policies, and compared with the state-of-the-art policy optimization methods.
@math _ t [ ' (a_t|s_t) Q (s_t,a_t) ] @math _ t [ R(s_t, a_t) ] @math _ t [D_ KL (d_ ^ ' (s_t,a_t) | d_ ^ (s_t,a_t)) ] @math _ t [ ( - R(s_t, a_t) ) ] @math _ [ w_ ' ( ) R( ) ] - d_2 (p( | ' ) | p( | )) N @math _ , [ R( ) ] @math _ , [ w_ ' ( ) R( ) ] @math _ , [w_ ' ( ) R( ) ] - d_2 ( ' | ) N @math d_ ^ (s_t,a_t)$ the state-action occupancy @cite_2 .
@cite_2
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!# @math ) 4 ' " + @math 4 ) @ & A B C D E . * . ! F ' G H ' IJ K L * M & + *) N z'cC g) ' &  p : q :  r Htd|#t9 ,s tvuw x yFz |;w]tS 9 x |;   C n+ U <dU' 4 2 K-8 mathematics students must learn many procedures, such as addition and subtraction. Students frequently learn "buggy' variations of these procedures, which we ideally could identify automatically. This is challenging because there are many possible variations that reflect deep compositions of procedural thought. Existing approaches for K-8 math use manually specified variations which do not scale to new math algorithms or previously unseen misconceptions. Our system examines students' answers and infers how they incorrectly combine basic skills into complex procedures. We evaluate this approach on data from approximately 300 students. Our system replicates 86 of the answers that contain clear systematic mistakes (13 ). Investigating further, we found 77 at least partially replicate a known misconception, with 53 matching exactly. We also present data from 29 participants showing that our system can demonstrate inferred incorrect procedures to an educator as successfully as a human expert. This paper presents the temporal logic of rewriting @math . Syntactically, @math is a very simple extension of @math which just adds action atoms, in the form of spatial action patterns, to @math . Semantically and pragmatically, however, when used together with rewriting logic as a "tandem" of system specification and property specification logics, it has substantially more expressive power than purely state-based logics like @math , or purely action-based logics like A- @math . Furthermore, it avoids the system property mismatch problem experienced in state-based or action-based logics, which makes many useful properties inexpressible in those frameworks without unnatural changes to a system's specification. The advantages in expresiveness of @math are gained without losing the ability to use existing tools and algorithms to model check its properties: a faithful translation of models and formulas is given that allows verifying @math properties with @math model checkers. Let @math be independent random positive variables and let @math , @math Let us denote [ P _1 + + _n < t = G_n (t). ]Theorem. [ t 1 - G_n (t) 1 - G(t) = n, n = 1,2,3, , ]if and only if [ t 1 - G_2 (t) 1 - G(t) = 2. ] This theorem is useful in some investigations of age-dependent branching processes.