Biological Cybernetics

, Volume 106, Issue 11–12, pp 757–765 | Cite as

Optimal isn’t good enough

  • Gerald E. LoebEmail author


The notion that biological systems come to embody optimal solutions seems consistent with the competitive drive of evolution. It has been used to interpret many examples of sensorimotor behavior. It is attractive from the viewpoint of control engineers because it solves the redundancy problem by identifying the one optimal motor strategy out of many similarly acceptable possibilities. This perspective examines whether there is sufficient basis to apply the formal engineering tools of optimal control to a reductionist understanding of biological systems. For an experimental biologist, this translates into whether the theory of optimal control generates nontrivial and testable hypotheses that accurately predict novel phenomena, ideally at deeper levels of structure than the observable behavior. The methodology of optimal control is applicable when there is (i) a single, known cost function to be optimized, (ii) an invertible model of the plant, and (iii) simple noise interfering with optimal performance. None of these is likely to be true for biological organisms. Furthermore, their motivation is usually good-enough rather than globally optimal behavior. Even then, the performance of a biological organism is often much farther from optimal than the physical limits of its hardware because the brain is continuously testing the acceptable limits of performance as well as just performing the task. This perspective considers an alternative strategy called “good-enough” control, in which the organism uses trial-and-error learning to acquire a repertoire of sensorimotor behaviors that are known to be useful, but not necessarily optimal. This leads to a diversity of solutions that tends to confer robustness on the individual organism and its evolution. It is also more consistent with the capabilities of higher sensorimotor structures, such as cerebral cortex, which seems to be designed to classify and recall complex sets of information, thereby allowing the organism to learn from experience, rather than to compute new strategies online. Optimal control has been a useful metaphor for understanding some superficial aspects of motor psychophysics. Reductionists who want to understand the underlying neural mechanisms need to move on.


Sensorimotor Optimal control Spinal cord Internal model Motor learning Feedback Cost Motor noise 


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  1. Anderson FC, Pandy MG (1999) A dynamic optimization solution for vertical jumping in three dimensions. Comput Methods Biomech Biomed Eng 2: 201–231CrossRefGoogle Scholar
  2. Bernstein NA (1967) The co-ordination and regulation of movement. In: Whiting HTA (ed) (Translation) Human motor actions: Bernstein reassessed. Elsevier, AmsterdamGoogle Scholar
  3. Bjursten LM, Norrsell K, Norrsell U (1976) Behavioural repertory of cats without cerebral cortex from infancy. Exp Brain Res 25: 115–130PubMedCrossRefGoogle Scholar
  4. Boyd SP, Vandenberghe L (2004) Convex optimization. Cambridge University Press, New YorkCrossRefGoogle Scholar
  5. Buchanan TS, Shreeve DA (1996) An evaluation of optimization techniques for the prediction of muscle activation patterns during isometric tasks. J Biomech Eng 118: 565–574PubMedCrossRefGoogle Scholar
  6. Churchland MM, Afshar A, Shenoy KV (2006) A central source of movement variability. Neuron 52: 1085–1096PubMedCentralPubMedCrossRefGoogle Scholar
  7. Crowninshield RD, Brand RA (1981) A physiologically based criterion of muscle force prediction in locomotion. J Biomech 14: 793–801PubMedCrossRefGoogle Scholar
  8. Culler E, Mettler FA (1934) Conditioned behavior in a decorticate dog. J Comp Psychol 18: 291–303CrossRefGoogle Scholar
  9. de Rugy A, Loeb GE, Carroll TJ (2012) Muscle coordination is habitual rather than optimal. J Neurosci 32: 7384–7391PubMedCrossRefGoogle Scholar
  10. Diamond IT (1979) The subdivisions of neocortex: a proposal to revise the traditional view of sensory, motor, and association areas. Prog Psychobiol Physiol Psychol 8: 1–43Google Scholar
  11. Flanders M (2011) What is the biological basis of sensorimotor integration?. Biol Cybern 104: 1–8PubMedCentralPubMedCrossRefGoogle Scholar
  12. Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5: 1688–1703PubMedGoogle Scholar
  13. Friston K (2010) The free-energy principle: a unified brain theory. Nat Rev Neurosci 11: 127–138PubMedCrossRefGoogle Scholar
  14. Gallistel CR, Fairhurst S, Balsam P (2004) The learning curve: implications of a quantitative analysis. Proc Natl Acad Sci USA 101: 13124–13131PubMedCentralPubMedCrossRefGoogle Scholar
  15. Gill PE, Murray W, Wright MH (1982) Practical optimization. Emerald Group Publishing Limited, West YorkshireGoogle Scholar
  16. Goaillard J-M, Taylor AL, Schulz DJ, Marder E (2009) Functional consequences of animal-to-animal variation in circuit parameters. Nat Neurosci 12: 1424–1430PubMedCentralPubMedCrossRefGoogle Scholar
  17. Grashow R, Brookings T, Marder E (2010) Compensation for variable intrinsic neuronal excitability by circuit-synaptic interactions. J Neurosci 30: 9145–9156PubMedCentralPubMedCrossRefGoogle Scholar
  18. Hamilton AFd, Jones KE (2004) The scaling of motor noise with muscle strength and motor unit number in humans. Exp Brain Res 157: 417–430PubMedCrossRefGoogle Scholar
  19. Harper D (2010) optimal. In: Online Etymology Dictionary.
  20. He J, Levine WS, Loeb GE (1991) Feedback gains for correcting small perturbations to standing posture. IEEE Trans Autom Control 36: 322–332CrossRefGoogle Scholar
  21. Jones KE, Hamilton AFd, Wolpert DM (2002) Sources of signal-dependent noise during isometric force production. J Neurophysiol 88: 1533–1544PubMedGoogle Scholar
  22. Kawato M (1999) Internal models for motor control and trajectory planning. Curr Opin Neurobiol 9: 718–727PubMedCrossRefGoogle Scholar
  23. Kawato M, Gomi H (1992) A computational model of four regions of the cerebellum based on feedback-error learning. BiolCybern 68: 95–103Google Scholar
  24. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J OPTIM 9: 112–147CrossRefGoogle Scholar
  25. Li Y, Levine WS, Loeb GE (2012) A two-joint human posture control model with realistic neural delays. IEEE Trans Neural Syst Rehabil Eng. doi: 10.1109/TNSRE.2012.2199333
  26. Loeb GE (1983) Finding common ground between robotics and physiology. Trends Neurosci 6: 203–204CrossRefGoogle Scholar
  27. Loeb GE (1993) The distal hindlimb musculature of the cat: interanimal variability of locomotor activity and cutaneous reflexes. Exp Brain Res 96: 125–140PubMedCrossRefGoogle Scholar
  28. Loeb GE (1999) Asymmetry of hindlimb muscle activity and cutaneous reflexes after tendon transfers in kittens. J Neurophysiol 82: 3392–3405PubMedGoogle Scholar
  29. Loeb GE, Levine WS, He J (1990) Understanding sensorimotor feedback through optimal control. Cold Spring Harbor Symp Quant Biol 55: 791–803PubMedCrossRefGoogle Scholar
  30. Marr D (1982) Vision. W.H. Freeman & Co, New YorkGoogle Scholar
  31. McCrea DA, Rybak IA (2008) Organization of mammalian locomotor rhythm and pattern generation. Brain Res Rev 57: 134–146PubMedCentralPubMedCrossRefGoogle Scholar
  32. Osu R, Gomi H (1999) Multijoint muscle regulation mechanisms examined by measured human arm stiffness and EMG signals. J Neurophysiol 81: 1458–1468PubMedGoogle Scholar
  33. Pandy MG, Anderson FC, Hull DG (1992) A parameter optimization approach for the optimal control of large-scale musculoskeletal systems. J Biomech Eng 114: 450–460PubMedCrossRefGoogle Scholar
  34. Pandy MG, Zajac FE, Sim E, Levine WS (1990) An optimal control model for maximum-height human jumping. J Biomech 23: 1185–1198PubMedCrossRefGoogle Scholar
  35. Partridge LD (1982) The good enough calculi of evolving control systems: evolution is not engineering. Am J Physiol 242: R173–R177PubMedGoogle Scholar
  36. Pedotti A, Krishnan VV, Stark L (1978) Optimization of muscle-force sequencing in human locomotion. Math Biosci 38: 57–76CrossRefGoogle Scholar
  37. Pellionisz AJ, Peterson BW (1988) A tensorial model of neck motor activation. In: Peterson BW, Richmond FJR (eds) Control of head movement. Oxford University Press, New York, pp 178–186Google Scholar
  38. Perfiliev S, Isa T, Johnels B, Steg G, Wessberg J (2010) Reflexive limb selection and control of reach direction to moving targets in cats, monkeys, and humans. J Neurophysiol 104: 2423–2432PubMedCrossRefGoogle Scholar
  39. Pierrot-Deseilligny E, Burke DC (2005) The circuitry of the human spinal cord: its role in motor control and movement disorders. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  40. Raikova RT, Gabriel DA, Aladjov H (2005) Experimental and modelling investigation of learning a fast elbow flexion in the horizontal plane. J Biomech 38: 2070–2077PubMedCrossRefGoogle Scholar
  41. Raphael G, Tsianos GA, Loeb GE (2010) Spinal-like regulator facilitates control of a two-degree-of-freedom wrist. J Neurosci 30: 9431–9444PubMedCrossRefGoogle Scholar
  42. Rathelot JA, Strick PL (2009) Subdivisions of primary motor cortex based on cortico-motoneuronal cells. PNAS 106: 918–923PubMedCentralPubMedCrossRefGoogle Scholar
  43. Sabes PN, Jordan MI (1997) Obstacle avoidance and a perturbation sensitivity model for motor planning. J Neurosci (New York) 17: 7119–7128Google Scholar
  44. Slifkin AB, Newell KM (1998) Is variability in human performance a reflection of system noise. Curr Dir Psychol Sci 7: 170–177CrossRefGoogle Scholar
  45. Tang LS, Goeritz ML, Caplan JS, Taylor AL, Fisek M, Marder E (2010) Precise temperature compensation of phase in a rhythmic motor pattern. PLoS Biol 8: e1000469PubMedCentralPubMedCrossRefGoogle Scholar
  46. Terekhov A, Zatsiorsky V (2011) Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods. Biol Cybern 104: 75–93PubMedCentralPubMedCrossRefGoogle Scholar
  47. Todorov E, Jordan MI (2002) Optimal feedback control as a theory of motor coordination. Nat Neurosci 5: 1226–1235PubMedCrossRefGoogle Scholar
  48. Tsianos GA, Raphael G, Loeb GE (2011) Modeling the potentiality of spinal-like circuitry for stabilization of a planar arm system. Prog Brain Res 194: 203–213PubMedCrossRefGoogle Scholar
  49. Tsianos GA, Rustin C, Loeb GE (2012) Mammalian muscle model for predicting force and energetics during physiological behaviors. IEEE Trans Neural Syst Rehabil Eng 20: 117–133PubMedCrossRefGoogle Scholar
  50. Valero-Cuevas FJ, Hoffmann H, Kurse MU, Kutch JJ, Theodorou EA (2009) Computational models for neuromuscular function. IEEE Rev Biomed Eng 2: 110–135PubMedCentralPubMedCrossRefGoogle Scholar
  51. Venkataraman P (2009) Applied optimization with MATLAB programming, Chapt 6. Wiley, SomersetGoogle Scholar
  52. Yuan G, Chang K, Hsieh C, Lin C (2010) A comparison of optimization methods for large-scale L1-regularized linear classification. Linear Classif J Mach Learn Res 2: 3183–3234Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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