Transition point dynamic programming (TPDP) is a memorybased, reinforcement learning, direct dynamic programming approach to adaptive optimal control that can reduce the learning time and memory usage required for the control of continuous stochastic dynamic systems. TPDP does so by determining an ideal set of transition points (TPs) which specify only the control action changes necessary for optimal control. TPDP converges to an ideal TP set by using a variation of Q-Iearning to assess the merits of adding, swapping and removing TPs from states throughout the state space. When applied to a race track problem, TPDP learned the optimal control policy much sooner than conventional Q-Iearning, and was able to do so using less memory. 1 INTRODUCTION Dynamic programming (DP) approaches can be utilized to determine optimal control policies for continuous stochastic dynamic systems when the state spaces of those systems have been quantized with a resolution suitable for control (Barto et al., 1991). DP controllers, in lheir simplest form, are memory-based controllers that operate by repeatedly updating cost values associated with every state in the discretized state space (Barto et al., 1991).

We analyze a simple hill-climbing algorithm (RMHC) that was previously shown to outperform a genetic algorithm (GA) on a simple "Royal Road" function. We then analyze an "idealized" genetic algorithm (IGA) that is significantly faster than RMHC and that gives a lower bound for GA speed. We identify the features of the IGA that give rise to this speedup, and discuss how these features can be incorporated into a real GA. 1 INTRODUCTION Our goal is to understand the class of problems for which genetic algorithms (GA) are most suited, and in particular, for which they will outperform other search algorithms. Several studies have empirically compared GAs with other search and optimization methods such as simple hill-climbing (e.g., Davis, 1991), simulated annealing (e.g., Ingber & Rosen, 1992), linear, nonlinear, and integer programming techniques, and other traditional optimization techniques (e.g., De Jong, 1975). However, such comparisons typically compare one version of the GA with a second algorithm on a single problem or set of problems, often using performance criteria which may not be appropriate.

In this paper, we show a reciprocal implementation of the "softmax" nonlinearity that is usually used to enforce local competition between neurons [Peterson, 1989]. We show that the circuit is passive and incrementally passive, and we explicitly compute its content and co-content functions. This circuit adds a new element to the library of the analog circuit designer that can be combined with reciprocal constraint boxes [Harris, 1988] and nonlinear resistive fuses [Harris, 1989] to form fast, analog VLSI optimization networks.

Stochastic optimization algorithms typically use learning rate schedules that behave asymptotically as J.t(t)

Two tightly coupled subproblems need to be solved for locating and recognizing the model: the correspondence problem (how are scene features put into correspondence with model features?),

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learning problems involving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DPbased learning algorithms to the powerful techniques of stochastic approximation via a new convergence theorem, enabling us to establish a class of convergent algorithms to which both TD("\) and Q-Iearning belong. 1 INTRODUCTION Learning to predict the future and to find an optimal way of controlling it are the basic goals of learning systems that interact with their environment. A variety of algorithms are currently being studied for the purposes of prediction and control in incompletely specified, stochastic environments. Here we consider learning algorithms defined in Markov environments. There are actions or controls (u) available for the learner that affect both the state transition probabilities, and the probability distribution for the immediate, state dependent costs (Ci(u)) incurred by the learner.

We analyze a simple hill-climbing algorithm (RMHC) that was previously shown to outperform a genetic algorithm (GA) on a simple "Royal Road" function. We then analyze an "idealized" genetic algorithm (IGA) that is significantly faster than RMHC and that gives a lower bound for GA speed. We identify the features of the IGA that give rise to this speedup, and discuss how these features can be incorporated into a real GA. 1 INTRODUCTION Our goal is to understand the class of problems for which genetic algorithms (GA) are most suited, and in particular, for which they will outperform other search algorithms. Several studies have empirically compared GAs with other search and optimization methods such as simple hill-climbing (e.g., Davis, 1991), simulated annealing (e.g., Ingber & Rosen, 1992), linear, nonlinear, and integer programming techniques, and other traditional optimization techniques (e.g., De Jong, 1975). However, such comparisons typically compare one version of the GA with a second algorithm on a single problem or set of problems, often using performance criteria which may not be appropriate.

Stochastic optimization algorithms typically use learning rate schedules that behave asymptotically as J.t(t)

Two tightly coupled subproblems need to be solved for locating and recognizing the model: the correspondence problem (how are scene features put into correspondence with model features?),

Transition point dynamic programming (TPDP) is a memorybased, reinforcement learning, direct dynamic programming approach to adaptive optimal control that can reduce the learning time and memory usage required for the control of continuous stochastic dynamic systems. TPDP does so by determining an ideal set of transition points (TPs) which specify only the control action changes necessary for optimal control. TPDP converges to an ideal TP set by using a variation of Q-Iearning to assess the merits of adding, swapping and removing TPs from states throughout the state space. When applied to a race track problem, TPDP learned the optimal control policy much sooner than conventional Q-Iearning, and was able to do so using less memory. 1 INTRODUCTION Dynamic programming (DP) approaches can be utilized to determine optimal control policies for continuous stochastic dynamic systems when the state spaces of those systems have been quantized with a resolution suitable for control (Barto et al., 1991). DP controllers, in lheir simplest form, are memory-based controllers that operate by repeatedly updating cost values associated with every state in the discretized state space (Barto et al., 1991).