Our objective functions include compositional and specialization hierarchies. We cast vision problems as inexact graph matching problems, formulate graph matching in terms of constrained optimization, and use analog neural networks to perform the optimization. The method is applicable to per(cid:173) ceptual grouping and model matching. Preliminary experimental results are shown.

A nonlinear neural framework, called the Generalized Hopfield network, is proposed, which is able to solve in a parallel distributed manner systems of nonlinear equations. The method is applied to the general nonlinear optimization problem. We demonstrate GHNs implementing the three most important optimization algorithms, namely the Augmented Lagrangian, Generalized Reduced Gradient and Successive Quadratic Programming methods. The study results in a dynamic view of the optimization problem and offers a straightforward model for the parallelization of the optimization computations, thus significantly extending the practical limits of problems that can be formulated as an optimization problem and which can gain from the introduction of nonlinearities in their structure (eg. The Hopfield computational model is almost exclusively applied to the solution of combinatorially complex linear decision problems (eg.

This paper explores whether analog circuitry can adequately per(cid:173) form constrained optimization. Constrained optimization circuits are designed using the differential multiplier method. Example circuits in(cid:173) clude a quadratic programming circuit and a constrained flip-flop.

Dyna architectures (Sutton, 1990) use learning algorithms to approximate the con(cid:173) ventional optimal control technique known as dynamic programming (DP) (Bell(cid:173) man, 1957; Bertsekas, 1987). DP itself is not a learning method, but rather a computational method for determining optimal behavior given a complete model of the task to be solved. It is very similar to state-space search, but differs in that it is more incremental and never considers actual action sequences explicitly, only single actions at a time. This makes DP more amenable to incremental planning at execution time, and also makes it more suitable for stochastic or incompletely modeled environments, as it need not consider the extremely large number of se(cid:173) quences possible in an uncertain environment.

A novel segmentation algorithm has been developed utilizing an absolute(cid:173) value smoothness penalty instead of the more common quadratic regu(cid:173) larizer. This functional imposes a piece-wise constant constraint on the segmented data. Since the minimized energy is guaranteed to be convex, there are no problems with local minima and no complex continuation methods are necessary to find the unique global minimum. By interpret(cid:173) ing the minimized energy as the generalized power of a nonlinear resistive network, a continuous-time analog segmentation circuit was constructed.

We use constrained optimization to select operating parameters for two circuits: a simple 3-transistor square root circuit, and an analog VLSI artificial cochlea. This automated method uses computer controlled mea(cid:173) surement and test equipment to choose chip parameters which minimize the difference between the actual circuit's behavior and a specified goal behavior. Choosing the proper circuit parameters is important to com(cid:173) pensate for manufacturing deviations or adjust circuit performance within a certain range. As biologically-motivated analog VLSI circuits become increasingly complex, implying more parameters, setting these parameters by hand will become more cumbersome. Thus an automated parameter setting method can be of great value [Fleischer 90].

Within a simple test-bed, application of feed-forward neurocontrol for short-term planning of robot trajectories in a dynamic environ(cid:173) ment is studied. The action network is embedded in a sensory(cid:173) motoric system architecture that contains a separate world model. It is continuously fed with short-term predicted spatio-temporal obstacle trajectories, and receives robot state feedback. It generates goal-directed motor actions - subject to the robot's kinematic and dynamic constraints - such that colli(cid:173) sions with moving obstacles are avoided. Using supervised learn(cid:173) ing, we distribute examples of the optimal planner mapping over a structure-level adapted parsimonious higher order network.

Stochastic optimization algorithms typically use learning rate schedules that behave asymptotically as J.t(t) J.to/t. The ensem(cid:173) ble dynamics (Leen and Moody, 1993) for such algorithms provides an easy path to results on mean squared weight error and asymp(cid:173) totic normality. We apply this approach to stochastic gradient algorithms with momentum. We show that at late times, learning is governed by an effective learning rate J.tejJ J.to/(l - f3) where f3 is the momentum parameter. We describe the behavior of the asymptotic weight error and give conditions on J.tejJ that insure optimal convergence speed.

Dynamic programming provides a methodology to develop planners and controllers for nonlinear systems. However, general dynamic programming is computationally intractable. We have developed procedures that allow more complex planning and control problems to be solved. We use second order local trajectory optimization to generate locally optimal plans and local models of the value function and its derivatives. We maintain global consistency of the local models of the value function, guaranteeing that our locally optimal plans are actually globally optimal, up to the resolution of our search procedures.

We analyze a simple hill-climbing algorithm (RMHC) that was pre(cid:173) viously 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.