Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision making and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations. While in standard control settings the sensors are assumed fixed, biological systems often gain from the extra flexibility of optimizing the sensors themselves. However, this sensory adaptation is geared towards control rather than perception, as is often assumed. In this work we show that sensory adaptation for control differs from sensory adaptation for perception, even for simple control setups. This implies, consistently with recent experimental results, that when studying sensory adaptation, it is essential to account for the task being performed.

Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision making and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations. While in standard control settings the sensors are assumed fixed, biological systems often gain from the extra flexibility of optimizing the sensors themselves. However, this sensory adaptation is geared towards control rather than perception, as is often assumed. In this work we show that sensory adaptation for control differs from sensory adaptation for perception, even for simple control setups. This implies, consistently with recent experimental results, that when studying sensory adaptation, it is essential to account for the task being performed.

First, let us start by the usual Stochastic Oscillator before proceeding with the Stochastic Smoothing Oscillator. An overbought level is an area where the market is perceived to be extremely bullish and is bound to consolidate. An oversold level is an area where market is perceived to be extremely bearish and is bound to bounce. Hence, the Stochastic Oscillator is a contrarian indicator that seeks to signal reactions of extreme movements.

Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision making and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations. While in standard control settings the sensors are assumed fixed, biological systems often gain from the extra flexibility of optimizing the sensors themselves. However, this sensory adaptation is geared towards control rather than perception, as is often assumed. In this work we show that sensory adaptation for control differs from sensory adaptation for perception, even for simple control setups. This implies, consistently with recent experimental results, that when studying sensory adaptation, it is essential to account for the task being performed.

While the theory of Optimal Control (OC) has become widely used as a framework for studying motor control, the standard framework of OC neglects many essential attributes of biological control [1, 2, 3]. The classic formulation of closed loop OC considers a dynamical system (plant) observed through sensors which transmit their output to a controller, which in turn selects a control law that drives actuators to steer the plant. This standard view, however, ignores the fact that sensors, controllers and actuators are often distributed across multiple subsystems, and disregards the communication channels between these subsystems. While the importance of jointly considering control and communication within a unified framework was already clear to the pioneers of the field of Cybernetics (e.g., Wiener and Ashby), it is only in recent years that increasing effort is being devoted to the formulation of a rigorous systems-theoretic framework for control and communication (e.g., [4]). Since the ultimate objective of an agent is to select appropriate actions, it is clear that sensation and communication must subserve effective control, and should be gauged by their contribution to action selection. In fact, given the communication constraints that plague biological systems (and many current distributed systems, e.g., cellular networks, sensor arrays, power grids, etc.), a major concern of a control design is the optimization of sensory information gathering and communication (consistently with theories of active perception). For example, recent theoretical work demonstrated a sharp communication bandwidth threshold below which control (or even stabilization) cannot be achieved (for a summary of such results see [4]). Moreover, when informational constraints exists within a control setting, even simple (linear and Gaussian) problems become nonlinear and intractable, as exemplified in the famous Witsenhausen counterexample [5]. The interdependence between sensation, communication and control is often overlooked both in control theory and in computational neuroscience, where one assumes that the overall solution to the control problem consists of first estimating the state of the controlled system (without reference to the control task), followed by constructing a controller based on the estimated state.