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Register a new userPolicy Optimization Using Semiparametric Models for Dynamic Pricing
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In this paper, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to Javanmard and Nazerzadeh [2019] except that we expand the demand curve to a semiparametric model and need to learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision-making policy that combines semiparametric estimation from a generalized linear model with an unknown link and online decision-making to minimize regret (maximize revenue). Under mild conditions, we show that for a market noise c.d.f. $F(cdot)$ with $m$-th order derivative ($mgeq 2$), our policy achieves a regret upper bound of $tilde{O}_{d}(T^{frac{2m+1}{4m-1}})$, where $T$ is time horizon and $tilde{O}_{d}$ is the order that hides logarithmic terms and the dimensionality of feature $d$. The upper bound is further reduced to $tilde{O}_{d}(sqrt{T})$ if $F$ is super smooth whose Fourier transform decays exponentially. In terms of dependence on the horizon $T$, these upper bounds are close to $Omega(sqrt{T})$, the lower bound where $F$ belongs to a parametric class. We further generalize these results to the case with dynamically dependent product features under the strong mixing condition.
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Feature-based dynamic pricing is an increasingly popular model of setting prices for highly differentiated products with applications in digital marketing, online sales, real estate and so on. The problem was formally studied as an online learning problem (Cohen et al., 2016; Javanmard & Nazerzadeh, 2019) where a seller needs to propose prices on the fly for a sequence of $T$ products based on their features $x$ while having a small regret relative to the best -- omniscient -- pricing strategy she could have come up with in hindsight. We revisit this problem and provide two algorithms (EMLP and ONSP) for stochastic and adversarial feature settings, respectively, and prove the optimal $O(dlog{T})$ regret bounds for both. In comparison, the best existing results are $Oleft(minleft{frac{1}{lambda_{min}^2}log{T}, sqrt{T}right}right)$ and $O(T^{2/3})$ respectively, with $lambda_{min}$ being the smallest eigenvalue of $mathbb{E}[xx^T]$ that could be arbitrarily close to $0$. We also prove an $Omega(sqrt{T})$ information-theoretic lower bound for a slightly more general setting, which demonstrates that knowing-the-demand-curve leads to an exponential improvement in feature-based dynamic pricing.
Standard dynamics models for continuous control make use of feedforward computation to predict the conditional distribution of next state and reward given current state and action using a multivariate Gaussian with a diagonal covariance structure. This modeling choice assumes that different dimensions of the next state and reward are conditionally independent given the current state and action and may be driven by the fact that fully observable physics-based simulation environments entail deterministic transition dynamics. In this paper, we challenge this conditional independence assumption and propose a family of expressive autoregressive dynamics models that generate different dimensions of the next state and reward sequentially conditioned on previous dimensions. We demonstrate that autoregressive dynamics models indeed outperform standard feedforward models in log-likelihood on heldout transitions. Furthermore, we compare different model-based and model-free off-policy evaluation (OPE) methods on RL Unplugged, a suite of offline MuJoCo datasets, and find that autoregressive dynamics models consistently outperform all baselines, achieving a new state-of-the-art. Finally, we show that autoregressive dynamics models are useful for offline policy optimization by serving as a way to enrich the replay buffer through data augmentation and improving performance using model-based planning.
The impacts of new real estate developments are strongly associated to its population distribution (types and compositions of households, incomes, social demographics) conditioned on aspects such as dwelling typology, price, location, and floor level. This paper presents a Machine Learning based method to model the population distribution of upcoming developments of new buildings within larger neighborhood/condo settings. We use a real data set from Ecopark Township, a real estate development project in Hanoi, Vietnam, where we study two machine learning algorithms from the deep generative models literature to create a population of synthetic agents: Conditional Variational Auto-Encoder (CVAE) and Conditional Generative Adversarial Networks (CGAN). A large experimental study was performed, showing that the CVAE outperforms both the empirical distribution, a non-trivial baseline model, and the CGAN in estimating the population distribution of new real estate development projects.
Policy search can in principle acquire complex strategies for control of robots and other autonomous systems. When the policy is trained to process raw sensory inputs, such as images and depth maps, it can also acquire a strategy that combines perception and control. However, effectively processing such complex inputs requires an expressive policy class, such as a large neural network. These high-dimensional policies are difficult to train, especially when learning to control safety-critical systems. We propose PLATO, an algorithm that trains complex control policies with supervised learning, using model-predictive control (MPC) to generate the supervision, hence never in need of running a partially trained and potentially unsafe policy. PLATO uses an adaptive training method to modify the behavior of MPC to gradually match the learned policy in order to generate training samples at states that are likely to be visited by the learned policy. PLATO also maintains the MPC cost as an objective to avoid highly undesirable actions that would result from strictly following the learned policy before it has been fully trained. We prove that this type of adaptive MPC expert produces supervision that leads to good long-horizon performance of the resulting policy. We also empirically demonstrate that MPC can still avoid dangerous on-policy actions in unexpected situations during training. Our empirical results on a set of challenging simulated aerial vehicle tasks demonstrate that, compared to prior methods, PLATO learns faster, experiences substantially fewer catastrophic failures (crashes) during training, and often converges to a better policy.
This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over standard model-reference adaptive control techniques is that it does not require the learned inverse model to be invertible at all instances of time. This enables the use of general function approximators to approximate the linearizing controller for the system without having to worry about singularities. However, the discrete-time and stochastic nature of these algorithms precludes the direct application of standard machinery from the adaptive control literature to provide deterministic stability proofs for the system. Nevertheless, we leverage these techniques alongside tools from the stochastic approximation literature to demonstrate that with high probability the tracking and parameter errors concentrate near zero when a certain persistence of excitation condition is satisfied. A simulated example of a double pendulum demonstrates the utility of the proposed theory. 1
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