Stochastic Compositional Optimization with Compositional Constraints

References

• Ahmed S, Çakmak U, Shapiro A (2007) Coherent risk measures in inventory problems. Eur. J. Oper. Res. 182(1):226–238.Google Scholar
• Balasubramanian K, Ghadimi S, Nguyen A (2022) Stochastic multilevel composition optimization algorithms with level-independent convergence rates. SIAM J. Optim. 32(2):519–544.Google Scholar
• Beck A (2017) First-Order Methods in Optimization (SIAM, Philadelphia).Google Scholar
• Bertsekas DP (1997) Nonlinear programming. J. Oper. Res. Soc. 48(3):334–334.Google Scholar
• Boob D, Deng Q, Lan G (2023) Stochastic first-order methods for convex and nonconvex functional constrained optimization. Math. Programming 197(1):215–279.Google Scholar
• Bruno S, Ahmed S, Shapiro A, Street A (2016) Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty. Eur. J. Oper. Res. 250(3):979–989.Google Scholar
• Chen T, Sun Y, Yin W (2021) Solving stochastic compositional optimization is nearly as easy as solving stochastic optimization. IEEE Trans. Signal Processing 69:4937–4948.Google Scholar
• Cole S, Giné X, Vickery J (2017) How does risk management influence production decisions? Evidence from a field experiment. Rev. Financial Stud. 30(6):1935–1970.Google Scholar
• Ermoliev Y (1988) Stochastic quasigradient methods. Ermoliev Y, Wets RJB, eds. Numerical Techniques for Stochastic Optimization (Springer-Verlag, New York), 141–186.Google Scholar
• Finn C, Abbeel P, Levine S (2017) Model-agnostic meta-learning for fast adaptation of deep networks. Internat. Conf. Machine Learn. (PMLR), 1126–1135.Google Scholar
• Finn C, Rajeswaran A, Kakade S, Levine S (2019) Online meta-learning. Chaudhuri K, Salakhutdinov R, eds. Proc. 36th Internat. Conf. Machine Learn., Proceedings of Machine Learning Research, vol. 97 (PMLR, New York), 1920–1930.Google Scholar
• Ge R, Huang F, Jin C, Yuan Y (2015) Escaping from saddle points—Online stochastic gradient for tensor decomposition. Grünwald P, Hazan E, Kale S, eds. Proc. 28th Conf. Learn. Theory, Proceedings of Machine Learning Research, vol. 40 (PMLR, Paris), 797–842.Google Scholar
• Ghadimi S, Ruszczynski A, Wang M (2020) A single timescale stochastic approximation method for nested stochastic optimization. SIAM J. Optim. 30(1):960–979.Google Scholar
• Haneveld WKK, Van Der Vlerk MH (2006) Integrated chance constraints: Reduced forms and an algorithm. CMS 3:245–269.Google Scholar
• Harvey CR, Liechty JC, Liechty MW, Müller P (2010) Portfolio selection with higher moments. Quant. Finance 10(5):469–485.Google Scholar
• Lan G, Zhou Z (2020) Algorithms for stochastic optimization with function or expectation constraints. Comput. Optim. Appl. 76(2):461–498.Google Scholar
• Lan G, Romeijn E, Zhou Z (2021) Conditional gradient methods for convex optimization with general affine and nonlinear constraints. SIAM J. Optim. 31(3):2307–2339.Google Scholar
• Lemaréchal C, Nemirovskii A, Nesterov Y (1995) New variants of bundle methods. Math. Programming 69(1):111–147.Google Scholar
• Lin Q, Nadarajah S, Soheili N, Yang T (2020) A data efficient and feasible level set method for stochastic convex optimization with expectation constraints. J. Machine Learn. Res. 21(1):1532–4435.Google Scholar
• Liu J, Cui Y, Pang JS (2022b) Solving nonsmooth and nonconvex compound stochastic programs with applications to risk measure minimization. Math. Oper. Res. 47(4):3051–3083.Link, Google Scholar
• Liu H, Wang X, So AMC (2022a) Adaptive coordinate sampling for stochastic primal–Dual optimization. Int. Trans. Oper. Res. 29(1):24–47.Google Scholar
• Madavan AN, Bose S (2021) A stochastic primal-dual method for optimization with conditional value at risk constraints. J. Optim. Theory Appl. 190(2):428–460.Google Scholar
• Nemirovski A, Juditsky A, Lan G, Shapiro A (2009) Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19(4):1574–1609.Google Scholar
• Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2(3):21–41.Google Scholar
• Ruszczynski A (2021) A stochastic subgradient method for nonsmooth nonconvex multilevel composition optimization. SIAM J. Control Optim. 59(3):2301–2320.Google Scholar
• Ruszczyński A, Shapiro A (2006) Optimization of convex risk functions. Math. Oper. Res. 31(3):433–452.Link, Google Scholar
• Slater M (2014) Lagrange multipliers revisited. Giorgi G, Kjeldsen TH, eds. Traces and Emergence of Nonlinear Programming (Springer, New York), 293–306.Google Scholar
• So AMC, Zhang J, Ye Y (2009) Stochastic combinatorial optimization with controllable risk aversion level. Math. Oper Res. 34(3):522–537.Link, Google Scholar
• Tan C, Zhang T, Ma S, Liu J (2018) Stochastic primal-dual method for empirical risk minimization with O(1) per-iteration complexity. Adv. Neural Inform. Processing Systems, vol. 31 (MIT Press, Cambridge, MA), 8376–8385.Google Scholar
• Wang M, Liu J (2016) A stochastic compositional gradient method using Markov samples. Proc . 2016 Winter Simulation Conf. (IEEE Press, Piscataway, NJ), 702–713.Google Scholar
• Wang M, Fang EX, Liu H (2017a) Stochastic compositional gradient descent: Algorithms for minimizing compositions of expected-value functions. Math. Programming 161(1–2):419–449.Google Scholar
• Wang M, Liu J, Fang EX (2017b) Accelerating stochastic composition optimization. J. Machine Learn. Res. 18(1):3721–3743.Google Scholar
• Yan Y, Xu Y, Lin Q, Zhang L, Yang T (2019) Stochastic primal-dual algorithms with faster convergence than o(1/T) for problems without bilinear structure. Preprint, submitted April 23, https://arxiv.org/abs/1904.10112.Google Scholar
• Yang S, Li X, Lan G (2024) Data-driven minimax optimization with expectation constraints. Oper. Res. 73(3):1151–1722.Google Scholar
• Yang S, Wang M, Fang EX (2019) Multilevel stochastic gradient methods for nested composition optimization. SIAM J. Optim. 29(1):616–659.Google Scholar
• Yu H, Neely M, Wei X (2017) Online convex optimization with stochastic constraints. Adv. Neural Inform. Processing Systems, vol. 30 (MIT Press, Cambridge, MA), 1427–1437.Google Scholar
• Zafar MB, Valera I, Gomez-Rodriguez M, Gummadi KP (2019) Fairness constraints: A flexible approach for fair classification. J. Machine Learn. Res. 20(1):2737–2778.Google Scholar
• Zhang Z, Lan G (2024) Optimal methods for convex nested stochastic composite optimization. Math. Programming, ePub ahead of print July 5, https://doi.org/10.1007/s10107-024-02090-3.Google Scholar
• Zhang J, Xiao L (2021) Multilevel composite stochastic optimization via nested variance reduction. SIAM J. Optim. 31(2):1131–1157.Google Scholar
• Zhang Z, Ahmed S, Lan G (2021) Efficient algorithms for distributionally robust stochastic optimization with discrete scenario support. SIAM J. Optim. 31(3):1690–1721.Google Scholar