Limits...
A Theory of Cheap Control in Embodied Systems.

Montúfar G, Ghazi-Zahedi K, Ay N - PLoS Comput. Biol. (2015)

Bottom Line: This embodied universal approximation is compared with the classical non-embodied universal approximation.To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines.The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.

ABSTRACT
We present a framework for designing cheap control architectures of embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

No MeSH data available.


Related in: MedlinePlus

Causal structure of the reactive SML.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4556690&req=5

pcbi.1004427.g002: Causal structure of the reactive SML.

Mentions: We have defined three mechanisms that are involved in a (reactive) sensorimotor loop of an embodied agent. Clearly, the agent’s embodiment poses constraints to this loop, which we attribute to the mechanisms β and α. The agent is equipped with these mechanisms, but they are both considered to be determined and not modifiable by the agent. On the other hand, the policy π can be modified by the agent in terms of learning processes. In order to describe the process of interaction of the agent with the world, we have to sequentially apply the individual mechanisms in the right order. Starting with an initial world state wt at time t, first the sensor state st is generated in terms of the channel β. Then, based on the state of the sensor, an actuator state at is chosen according to the policy π. Finally, the world makes a transition, governed by α, from the state wt to a new state wt+1, which is influenced by the actuator state at of the agent. Altogether, this defines the combined mechanismℙπ(wt;dst,dat,dwt+1)≔β(wt;dst)π(st;dat)α(wt,at;dwt+1).(1)Note that we consider β and α fixed and therefore emphasize only the dependence on π. Now, with the new state wt+1 of the world, the three steps are iterated. This generates a process which is shown in Fig 2. Formally, the process is a probability distribution over trajectories that start with w0:w0,s0,a0,w1,s1,a1,w2,s2,a2,w3,…,sT-1,aT-1,wT.(2)In order to describe this probability distribution, we have to iterate the mechanism Eq (1) by multiplication:ℙπ(w0;ds0,da0,dw1,…,dsT-1,daT-1,dwT)≔∏t=0T-1ℙπ(wt;dst,dat,dwt+1).(3)


A Theory of Cheap Control in Embodied Systems.

Montúfar G, Ghazi-Zahedi K, Ay N - PLoS Comput. Biol. (2015)

Causal structure of the reactive SML.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4556690&req=5

pcbi.1004427.g002: Causal structure of the reactive SML.
Mentions: We have defined three mechanisms that are involved in a (reactive) sensorimotor loop of an embodied agent. Clearly, the agent’s embodiment poses constraints to this loop, which we attribute to the mechanisms β and α. The agent is equipped with these mechanisms, but they are both considered to be determined and not modifiable by the agent. On the other hand, the policy π can be modified by the agent in terms of learning processes. In order to describe the process of interaction of the agent with the world, we have to sequentially apply the individual mechanisms in the right order. Starting with an initial world state wt at time t, first the sensor state st is generated in terms of the channel β. Then, based on the state of the sensor, an actuator state at is chosen according to the policy π. Finally, the world makes a transition, governed by α, from the state wt to a new state wt+1, which is influenced by the actuator state at of the agent. Altogether, this defines the combined mechanismℙπ(wt;dst,dat,dwt+1)≔β(wt;dst)π(st;dat)α(wt,at;dwt+1).(1)Note that we consider β and α fixed and therefore emphasize only the dependence on π. Now, with the new state wt+1 of the world, the three steps are iterated. This generates a process which is shown in Fig 2. Formally, the process is a probability distribution over trajectories that start with w0:w0,s0,a0,w1,s1,a1,w2,s2,a2,w3,…,sT-1,aT-1,wT.(2)In order to describe this probability distribution, we have to iterate the mechanism Eq (1) by multiplication:ℙπ(w0;ds0,da0,dw1,…,dsT-1,daT-1,dwT)≔∏t=0T-1ℙπ(wt;dst,dat,dwt+1).(3)

Bottom Line: This embodied universal approximation is compared with the classical non-embodied universal approximation.To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines.The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.

ABSTRACT
We present a framework for designing cheap control architectures of embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

No MeSH data available.


Related in: MedlinePlus