Performance Dynamics and Termination Errors in Reinforcement Learning: A Unifying Perspective

In reinforcement learning, a decision needs to be made at some point as to whether it is worthwhile to carry on with the learning process or to terminate it. In many such situations, stochastic elements are often present which govern the occurrence of rewards, with the sequential occurrences of positive rewards randomly interleaved with negative rewards. For most practical learners, the learning is considered useful if the number of positive rewards always exceeds the negative ones. A situation that often calls for learning termination is when the number of negative rewards exceeds the number of positive rewards. However, while this seems reasonable, the error of premature termination, whereby termination is enacted along with the conclusion of learning failure despite the positive rewards eventually far outnumber the negative ones, can be significant. In this paper, using combinatorial analysis we study the error probability in wrongly terminating a reinforcement learning activity which undermines the effectiveness of an optimal policy, and we show that the resultant error can be quite high. Whilst we demonstrate mathematically that such errors can never be eliminated, we propose some practical mechanisms that can effectively reduce such errors. Simulation experiments have been carried out, the results of which are in close agreement with our theoretical findings.Comment: Short Paper in AIKE 201

Sensitivity of the LHC to Electroweak Symmetry Breaking: Equivalence Theorem as a Criterion

Based upon our recent study on the intrinsic connection between the longitudinal weak-boson scatterings and probing the electroweak symmetry breaking (EWSB) mechanism, we reveal the profound physical content of the Equivalence Theorem (ET) as being able to discriminate physical processes which are sensitive/insensitive to probing the EWSB sector. With this physical content of the ET as a criterion, we analyze the complete set of the bosonic operators in the electroweak chiral Lagrangian and systematically classify the sensitivities to probing all these operators at the CERN LHC via the weak-boson fusion in $W^\pm W^\pm$ channel. This is achieved by developing a precise power counting rule (a generalization from Weinberg's counting method) to {\it separately} count the power dependences on the energy $E$ and all relevant mass scales.Comment: 33 pages, LaTeX, 10 figures and Table-1b are in the separate file figtab.uu. (The only change made from the previous version is to fix the bugs in the uuencoded file.

Probing Electroweak Symmetry Breaking Mechanism at the LHC: A Guideline from Power Counting Analysis

We formulate the equivalence theorem as a theoretical criterion for sensitively probing the electroweak symmetry breaking mechanism, and develop a precise power counting method for the chiral Lagrangian formulated electroweak theories. Armed with these, we perform a systematic analysis on the sensitivities of the scattering processes $W^\pm W^\pm \rightarrow W^\pm W^\pm$ and $q\bar{q}'\rightarrow W^\pm Z$ for testing all possible effective bosonic operators in the chiral Lagrangian formulated electroweak theories at the CERN Large Hadron Collider (LHC). The analysis shows that these two kinds of processes are "complementary" in probing the electroweak symmetry breaking sector.Comment: Extended version, 11-page-Latex-file and 3 separate PS-Figs. To be Published in Mod.Phys.Lett.

Longitudinal/Goldstone boson equivalence and phenomenology of probing the electroweak symmetry breaking

We formulate the equivalence between the longitudinal weak-boson and the Goldstone boson as a criterion for sensitively probing the electroweak symmetry breaking mechanism and develop a precise power counting rule for chiral Lagrangian formulated electroweak theories. With these we semi-quatitatively analyze the sensitivities to various effective operators related to electrowaeak symmetry breaking via weak-boson scatterings at the CERN Large Hadron Collider (LHC).Comment: 6 pages, LaTex, 1 postscript figure included using psfig.te

Stochastic Reinforcement Learning

In reinforcement learning episodes, the rewards and punishments are often non-deterministic, and there are invariably stochastic elements governing the underlying situation. Such stochastic elements are often numerous and cannot be known in advance, and they have a tendency to obscure the underlying rewards and punishments patterns. Indeed, if stochastic elements were absent, the same outcome would occur every time and the learning problems involved could be greatly simplified. In addition, in most practical situations, the cost of an observation to receive either a reward or punishment can be significant, and one would wish to arrive at the correct learning conclusion by incurring minimum cost. In this paper, we present a stochastic approach to reinforcement learning which explicitly models the variability present in the learning environment and the cost of observation. Criteria and rules for learning success are quantitatively analyzed, and probabilities of exceeding the observation cost bounds are also obtained.Comment: AIKE 201