SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Therefore, the same as  $\mathbf{query}(x) = w_x$ ,  $\mathbf{query}(x) \geq w_x$  also divides the unchecked items into two parts, and the user is supposed to answer Yes or No, corresponding to either one of the two parts. Then, Proposition 2 also works here. Namely, for each attribute  $x \in \mathcal{X}_{k-1}$ , the oracle  $w_x$ , denoted as  $w_x^0$ , is the one that can partition the relevance scores into two equal parts. Formally, we have:
$$
w _ {x} ^ {0} = \underset {w _ {x} \in \mathbb {R}} {\arg \min } \left\| \operatorname {S U M} \left(\left\{\Psi_ {\mathrm {R E}} \left(v _ {m}\right) \mid v _ {m} \in \mathcal {V} _ {x \geq w _ {x}} \cap \mathcal {V} _ {k - 1} \right\}\right) - \frac {\operatorname {S U M} \left(\left\{\Psi_ {\mathrm {R E}} \left(v _ {m ^ {\prime}}\right) \mid v _ {m ^ {\prime}} \in \mathcal {V} _ {k - 1} \right\}\right)}{2} \right\|. \tag {29}
$$
Since it is infeasible to find an exact oracle one, we approximate  $w_{x}^{0}$  as:
$$
w _ {x} = \text {A V E R A G E} \left(\left\{\Psi_ {\mathrm {R E}} \left(v _ {m}\right) \cdot w _ {v _ {m}} \mid v _ {m} \in \mathcal {V} _ {k - 1} \right\}\right), \tag {30}
$$
where  $w_{v_m}$  is the value of attribute  $x$  in item  $v_m$ . It indicates that our estimation is the average of the attribute values for the items in  $\mathcal{V}_{k-1}$  weighted by their relevance scores.
A2.2 Making  $\Psi_{\mathrm{CG}}(\cdot)$  Consider Dependence among Attributes
The following techniques allow CORE to take the dependence among attributes into account. We provide two ways, where one requires an FM-based recommender system, while the other one poses no constraint.
Taking  $\Psi_{\mathbb{CG}}(\cdot)$  in Eq. (6) as an example, we re-formulate Eq. (6) as, when  $a \in \mathcal{X}_{k-1}$ , and then we can compute  $\Psi_{\mathbb{CG}}(\text{query}(a))$  as:
$$
\Psi_ {\mathrm {C G}} ^ {\mathrm {D}} (\operatorname {q u e r y} (a)) = \sum_ {a ^ {\prime} \in \mathcal {A}} \left(\Psi_ {\mathrm {C G}} (\operatorname {q u e r y} \left(a ^ {\prime}\right)) \cdot \Pr (\operatorname {q u e r y} \left(a ^ {\prime}\right) | \operatorname {q u e r y} (a))\right), \tag {31}
$$
where we use  $\Psi_{\mathrm{CG}}^{\mathrm{D}}(\cdot)$  to denote this variant of  $\Psi_{\mathrm{CG}}(\cdot)$ .
Estimation from a Pre-trained FM-based Recommender System. If our recommender system applies a factorization machine (FM) based recommendation approach, then we can directly adopt the learned weights as the estimation of  $\operatorname{Pr}(\mathbf{query}(a')|\mathbf{query}(a))$  in Eq. (31). Taking DeepFM [20] as an example, we begin by recapping its FM component:
$$
y _ {\mathrm {F M}} = w _ {0} + \sum_ {n = 1} ^ {N} w _ {n} x _ {n} + \sum_ {n = 1} ^ {N} \sum_ {n ^ {\prime} = n + 1} ^ {N} \left\langle \mathbf {v} _ {n}, \mathbf {v} _ {n ^ {\prime}} \right\rangle x _ {n} x _ {n ^ {\prime}}, \tag {32}
$$
where the model parameters should be estimated in the recommender system (in line 1 in Algorithm 1), including  $w_0 \in \mathbb{R}$ ,  $\mathbf{w} \in \mathbb{R}^N$ ,  $\mathbf{V} \in \mathbb{R}^{N \times D}$  and  $D$  is the dimension of embedding. And,  $\langle \cdot, \cdot \rangle$  is the dot product of two vectors of size  $D$ , defined as  $\langle \mathbf{v}_i, \mathbf{v}_j \rangle = \sum_{d=1}^{D} v_{id} \cdot v_{jd}$ . In this regard, for each pair of attributes (e.g.,  $(a, a')$  in Eq. (31)), we can find the corresponding normalized  $\langle \mathbf{v}_n, \mathbf{v}_{n'} \rangle / |\mathbf{v}_n| \cdot |\mathbf{v}_{n'}|$  as the estimation of  $\operatorname*{Pr}(\text{query}(a')) | \text{query}(a)$ .
Estimation in a Statistical Way. If applying any other recommendation approach to the recommender system, we design a statistical way. We first decompose  $\Psi_{\mathrm{CG}}^{\mathrm{D}}(\mathrm{query}(a))$  according to Eq. (6):
$$
\left. \Psi_ {\mathbb {C G}} ^ {\mathrm {D}} (\operatorname {q u e r y} (a)) = \sum_ {w _ {a} \in \mathcal {W} _ {a}} \left(\Psi_ {\mathbb {C G}} ^ {\mathrm {D}} \left(w _ {a} = w _ {a} ^ {*}\right) \cdot \Pr \left(w _ {a} = w _ {a} ^ {*}\right)\right), \right. \tag {33}
$$
where we define  $\Psi_{\mathbb{CG}}^{\mathrm{D}}(w_a = w_a^*)$  as:
$$
\Psi_ {\mathbb {C G}} ^ {\mathrm {D}} \left(w _ {a} = w _ {a} ^ {*}\right) = \sum_ {a ^ {\prime} \in \mathcal {A}} \sum_ {w _ {a ^ {\prime}} \in \mathcal {W} _ {a ^ {\prime}}} \left(\Psi_ {\mathbb {C G}} \left(w _ {a ^ {\prime}} = w _ {a ^ {\prime}} ^ {*}\right) \cdot \Pr \left(w _ {a ^ {\prime}} = w _ {a ^ {\prime}} ^ {*} \mid w _ {a} = w _ {a} ^ {*}\right)\right), \tag {34}
$$
where  $\operatorname*{Pr}(w_{a'} = w_{a'}^* | w_a = w_a^*)$  measures the probability of how likely getting the user's preference on attribute  $a$  (i.e.,  $w_a = w_a^*$ ) determines the user's preference on other attributes (i.e.,  $w_{a'} = w_{a'}^*$ ). For example, in Figure 1, if the user's preference on attribute Hotel Level is 5 (i.e.,  $a$  is Hotel Level,  $w_a$  is 5 and the user's answer is Yes), then we could be confident to say that the user preference on attribute Shower Service is Yes (i.e.,  $a'$  is Shower Service,  $w_{a'}$  is Yes, and the user's answer is Yes), i.e.,  $\operatorname*{Pr}(w_{a'} = w_{a'}^* | w_a = w_a^*)$  is close to 1.
We estimate  $\Pr (w_{a'} = w_{a'}^* |w_a = w_a^*)$  by using the definition of the conditional probability:
$$
\Pr \left(w _ {a ^ {\prime}} = w _ {a ^ {\prime}} ^ {*} \mid w _ {a} = w _ {a} ^ {*}\right) = \frac {\left| \mathcal {V} _ {\left(a _ {\text {v a l u e}} = w _ {a}\right) \wedge \left(a _ {\text {v a l u e}} ^ {\prime} = w _ {a ^ {\prime}}\right)} \cap \mathcal {V} _ {k - 1} \right|}{\left| \mathcal {V} _ {a _ {\text {v a l u e}}} = w _ {a} \cap \mathcal {V} _ {k - 1} \right|}, \tag {35}
$$
where  $\mathcal{V}_{a_{\mathrm{value}} = w_a}$  is the set of items whose value of  $a$  equals  $w_{a}$ , and  $\mathcal{V}_{(a_{\mathrm{value}} = w_a)\wedge (a_{\mathrm{value}}^{\prime} = w_{a^{\prime}})}$  is the set of items whose value of  $a$  equals  $w_{a}$  and value of  $a^\prime$  equals  $w_{a^\prime}$ . By incorporating Eqs. (34) and (35) into Eq. (33), we can compute  $\Psi_{\mathrm{CG}}^{\mathrm{D}}(\mathrm{query}(a))$  for any  $a\in \mathcal{X}_{k - 1}$ .
Extensions to Other Cases. Besides querying attributes, we also introduce another querying strategy to query attribute values. Formally, we can have:
$$
\Psi_ {\mathrm {C G}} ^ {\mathrm {D}} (\text {q u e r y} (x) = w _ {a}) = \Psi_ {\mathrm {C G}} ^ {\mathrm {D}} \left(w _ {x} = w _ {x} ^ {*}\right) \cdot \Pr \left(w _ {x} = w _ {x} ^ {*}\right) + \Psi_ {\mathrm {C G}} ^ {\mathrm {D}} \left(w _ {x} \neq w _ {x} ^ {*}\right) \cdot \Pr \left(w _ {x} \neq w _ {x} ^ {*}\right), \tag {36}
$$
where  $\Psi_{\mathbb{CG}}^{\mathsf{D}}(w_x = w_x^*)$  can be computed by Eq. (34), and the formulation of  $\Psi_{\mathbb{CG}}^{\mathsf{D}}(w_x \neq w_x^*)$  could be directly extended from Eq. (34) by replacing  $\Psi_{\mathbb{CG}}(w_x = w_x^*)$  with  $\Psi_{\mathbb{CG}}(w_x \neq w_x^*)$ , and replacing  $\operatorname*{Pr}(w_{a'} = w_{a'}^* | w_a = w_a^*)$  with  $\operatorname*{Pr}(w_{a'} \neq w_{a'}^* | w_a \neq w_a^*)$ .  $\operatorname*{Pr}(w_{a'} \neq w_{a'}^* | w_a \neq w_a^*)$  could be computed by replacing  $\mathcal{V}_{a\_value} = w_a$  with  $\mathcal{V}_{a\_value} \neq w_a$ , and replacing  $\mathcal{V}_{(a\_value = w_a) \land (a'_value = w'_a)}$  with
$\mathcal{V}_{(a_{\mathrm{value}} \neq w_a) \wedge (a_{\mathrm{value}}' \neq w_{a'})}$ .  $\mathcal{V}_{a_{\mathrm{value}} \neq w_a}$  is the set of items whose value of  $a$  does not equal  $w_a$ , and  $\mathcal{V}_{(a_{\mathrm{value}} \neq w_a) \wedge (a_{\mathrm{value}}' \neq w_{a'})}$  is the set of items whose value of  $a$  does not equal  $w_a$  and value of  $a'$  does not equal  $w_{a'}$ .
Then, we have made our conversational agent consider the dependence among attributes for cases (ii) and (iii), summarized in Definition A1. There is no need to consider the dependence in case (i), and, as concluded in Appendix A1.1, (iv) can be regarded as a special engineering technique in (iii), and thus, one just needs to follow the same way to handle case (iv).
A2.3 Overall Algorithm
We summarize the overall algorithm in Algorithm 1. CORE follows an offline-training-and-online-checking paradigm, where offline-training is represented in lines 1 and 12, and online-checking is represented in lines 5, 6 and 7.
As shown in line 5, there are two querying settings, i.e., querying items and attributes, and querying items and attribute values. We note that querying attributes and querying attribute values can be compatible, but can not simultaneously operate on the same attribute. We recap that Proposition 1 says that for each attribute, assuming users could give a clear answer showing their preference, querying an attribute can always obtain certainty gain not smaller than querying any attribute value of the attribute.
Therefore, in practice, we would select those attributes that are likely to receive a clear preference from users (e.g., attributes Category, Brand) in the setting of querying items and attributes, and use the rest of attributes (e.g., attribute Price) in the setting of querying items and attribute values. Also, as stated at the end of Appendix A1.1, we can further select several attributes with a small space of attribute values, use them in the setting of querying items and attributes, and list all the candidate attribute values in the queries. In this regard, for any attribute, since the space of attribute values is changing in the context of querying attribute values, then we may transfer from the setting of querying attribute values to querying attributes, when there are few unchecked candidate attribute values.
All the above operations need careful feature engineering, which should be task-specific and dataset-specific. We argue that this is out of the scope of this paper, and we leave it for future work.
A3 Experimental Configuration
A3.1 Dataset Descriptions and Data Pre-processing
We summarize the datasets used in this paper as follows.
- Amazon dataset [8, 33] is a dataset collected by Amazon from May 1996 to July 2014. There are 1,114,563 reviews of 133,960 users and 431,827 items and 6 attributes.
- LastFM dataset [9] is a dataset collected from Lastfm, a music artist recommendation platform. There are 76,693 interactions of 1,801 users and 7,432 items and 33 attributes.
- Yelp dataset [12] is a dataset collected from Yelp, a business recommendation platform. There are 1,368,606 interactions of 27,675 users and 70,311 items and 590 attributes. We follow [30] to create 29 (parents) attributes upon 590 original attributes, and we use the newly created ones in our experiments.
- Taobao dataset [10] is a dataset collected by Taobao from November 2007 to December 2007. It consists of 100,150,807 interactions of 987,994 users and 4,162,024 items with an average sequence length of 101 and 4 attributes.
- Tmall dataset [11] is a dataset collected by Tmall from May 2015 to November 2015. It consists of 54,925,331 interactions of 424,170 users and 1,090,390 items with an average length of 129 and 9 attributes.
- Alipay dataset [7] is a dataset collected by Alipay, from July 2015 to November 2015. There are 35,179,371 interactions of 498,308 users and 2,200,191 items with an average sequence length of 70 and 6 attributes.
- Douban Movie dataset [35, 53] is a dataset collected from Douban Movie, a movie recommendation platform. There are 1,278,401 interactions of 2,712 users and 34,893 items with 4 attributes.
Table A1: Results comparison in the context of querying attributes and items on tabular datasets.
ΨRE(·)	ΨCD(·)	Amazon	LastFM	Yelp
T@3	S@3	T@5	S@5	T@3	S@3	T@5	S@5	T@3	S@3	T@5	S@5
COLD START	AG	6.47	0.12	7.83	0.23	6.77	0.05	8.32	0.14	6.65	0.08	8.29	0.13
ME	3.04	0.98	5.00	1.00	3.00	1.00	5.00	1.00	3.00	1.00	5.00	1.00
CORE	2.88	1.00	2.87	1.00	2.73	1.00	2.75	1.00	2.92	1.00	2.94	1.00
CORED+	2.84	1.00	2.86	1.00	2.74	1.00	2.73	1.00	2.90	1.00	2.91	1.00
FM	AG	2.76	0.74	2.97	0.83	4.14	0.52	4.67	0.64	3.29	0.70	3.39	0.81
CRM	3.07	0.98	3.37	0.83	2.98	0.99	3.43	1.00	3.08	0.98	3.12	0.96
EAR	2.98	0.99	3.13	1.00	3.02	1.00	3.51	1.00	2.94	1.00	3.02	0.99
CORE	2.17	1.00	2.16	1.00	2.06	1.00	2.07	1.00	2.09	1.00	2.10	1.00
CORED+	2.14	1.00	2.14	1.00	2.05	1.00	2.05	1.00	2.10	1.00	2.08	1.00
DEEP FM	AG	3.07	0.71	3.27	0.82	3.50	0.68	3.84	0.79	3.09	0.74	3.11	0.88
CRM	2.68	0.99	2.99	0.99	2.94	0.99	3.05	0.99	2.92	1.00	2.99	1.00
EAR	2.70	1.00	2.88	1.00	2.95	1.00	3.21	0.98	2.87	1.00	2.97	1.00
CRIF	2.84	1.00	2.64	1.00	2.78	0.99	2.81	1.00	2.93	0.99	2.01	0.99
UNICORN	2.65	1.00	2.45	1.00	2.87	1.00	2.90	1.00	2.88	1.00	2.92	1.00
CORE	2.07	1.00	2.06	1.00	2.07	1.00	2.08	1.00	2.06	1.00	2.07	1.00
CORED+	2.08	1.00	2.02	1.00	2.05	1.00	2.03	1.00	2.03	1.00	2.06	1.00
PNN	AG	3.02	0.74	3.10	0.87	3.44	0.67	3.53	0.84	2.83	0.77	2.82	0.91
CORE	2.71	1.00	3.00	1.00	2.05	1.00	2.06	1.00	2.15	1.00	2.16	1.00
CORED+	2.68	1.00	2.98	1.00	2.07	1.00	2.02	1.00	2.08	1.00	2.11	1.00
- Douban Book dataset [35, 53] is a dataset collected from Douban Book, a book recommendation platform. There are 96,041 interactions of 2,110 users and 6,777 items with 5 attributes.
In summary, our paper includes three tubular datasets (i.e., Amazon, LastFM, Yelp), three sequential datasets (i.e., Taobao, Tmall, Alipay), and two graph-structured datasets (i.e., Douban Book, Douban Movie). First, we follow the common setting of recommendation evaluation [22, 39] that reduces the data sparsity by pruning the users that have less than 10 historical interactions and the users that have at least 1 positive feedback (e.g., clicks in Taobao). We construct each session by sampling one user and 30 items from her browsing log (if less than 30 items, we randomly sample some items that are not browsed, as the items receive negative feedback, into the session). During sampling, we manage the ratio of the number of items receiving positive feedback and the number of negative feedback falls into the range from 1:10 to 1:30. We use a one-to-one mapping function to map all the attribute values into a discrete space to operate. From those attributes with continuous spaces, we directly apply our proposed method introduced in Section 3.2.
A3.2 Simulator Design
As summarized in Definition A1, there are two main agents in our simulator, namely a conversational agent and a user agent. The conversational agent is given the set of candidate items (i.e.,  $\mathcal{V}$ ), and the set of candidate attributes (i.e.,  $\mathcal{X}$ ) (together with their candidate values, i.e.,  $\mathcal{W}_x$  for every  $x \in \mathcal{X}$ ). Then, at  $k$ -th turn, the conversational agent is supposed to provide an action of querying, either one from (i), (ii), (iii) and (iv) shown in Definition A1, and the user agent is supposed to generate the corresponding answer and derive the set of unchecked items (i.e.,  $\mathcal{V}_k$ ), and the set of unchecked attributes (i.e.,  $\mathcal{X}_k$ ) (together with the unchecked values of each attribute  $x$ ). Let  $\mathcal{W}_x^k$  be the set of the unchecked values of  $x$ , then its update function is simple. Firstly, we assign  $\mathcal{W}_x^0 = \mathcal{W}_x$ , and we can further define  $\Delta \mathcal{W}_x^k = \mathcal{W}_x^{k-1} \setminus \mathcal{W}_x^k$ , then  $\Delta \mathcal{W}_x^k$  can be written as:
$$
\Delta \mathcal {W} _ {x} ^ {k} = \left\{ \begin{array}{c c} \left\{w _ {x} \right\}, & \text {q u e r y i n g (i i i) , a n d s e l e c t i n g a n a t t r i b u t e v a l u e i n x ,} \\ \emptyset , & \text {o t h e r w i s e .} \end{array} \right. \tag {37}
$$
For simplicity, we omit the above update in the main text.
From the above description, we know that the conversational agent and the user agent are communicating through exchanging the set of unchecked items and unchecked attributes (and unchecked attribute values). We also develop a port function in the conversational agent that leverages a pre-trained large language model to generate the human text for each action. See Appendix A4.2 for detailed descriptions and examples.
Table A2: Results comparison of querying attribute values and items on tabular datasets.
ΨRE(·)	ΨCO(·)	Amazon	LastFM	Yelp
T@3	S@3	T@5	S@5	T@3	S@3	T@5	S@5	T@3	S@3	T@5	S@5
COLD START	AG	6.47	0.12	7.83	0.23	6.77	0.05	8.32	0.14	6.65	0.08	8.29	0.13
ME	6.50	0.12	8.34	0.16	6.84	0.04	8.56	0.11	6.40	0.15	8.18	0.20
CORE	6.02	0.25	6.18	0.65	5.84	0.29	5.72	0.74	5.25	0.19	6.23	0.65
CORED+	6.00	0.26	6.01	0.67	5.79	0.30	5.70	0.75	5.02	0.21	6.12	0.68
FM	AG	2.76	0.74	2.97	0.83	4.14	0.52	4.67	0.64	3.29	0.70	3.39	0.81
CRM	4.58	0.28	6.42	0.38	4.23	0.34	5.87	0.63	4.12	0.25	6.01	0.69
EAR	4.13	0.32	6.32	0.42	4.02	0.38	5.45	0.67	4.10	0.28	5.95	0.72
CRIF	4.34	0.28	6.24	0.45	3.98	0.58	4.11	0.76	4.07	0.31	6.02	0.70
UNICORN	4.43	0.30	6.15	0.52	4.00	0.54	7.56	0.11	4.40	0.25	5.38	0.77
CORE	3.26	0.83	3.19	0.99	3.79	0.72	3.50	0.99	3.14	0.84	3.20	0.99
CORED+	3.16	0.85	3.22	1.00	3.75	0.74	3.53	1.00	3.10	0.85	3.23	1.00
DEEP FM	AG	3.07	0.71	3.27	0.82	3.50	0.68	3.84	0.79	3.09	0.74	3.11	0.88
CRM	4.51	0.29	6.32	0.40	4.18	0.38	5.88	0.63	4.11	0.23	6.02	0.71
EAR	4.47	0.30	6.35	0.43	4.01	0.37	5.43	0.69	4.01	0.32	5.74	0.75
CORE	3.23	0.85	3.22	0.99	3.47	0.81	3.34	1.00	2.98	0.93	3.11	1.00
CORED+	3.16	0.87	3.21	1.00	3.45	0.83	3.30	1.00	2.97	0.94	3.10	1.00
PNN	AG	3.02	0.74	3.10	0.87	3.44	0.67	3.53	0.84	2.83	0.77	2.82	0.91
CORE	3.01	0.88	3.04	0.99	3.10	0.87	3.20	0.99	2.75	0.88	2.76	1.00
CORED+	3.00	0.92	3.04	1.00	3.05	0.88	3.12	1.00	2.74	0.88	2.76	1.00
A3.3 Baseline Descriptions
We first summarize the recommendation approaches, denoted as  $\Psi_{\mathrm{RE}}(\cdot)$ , used in this paper as follows.
- COLD START denotes the cold-start setting, where all the relevance scores of items are uniformly generated. In other words, for the item set  $\mathcal{V} = \{v_m\}_{m=1}^M$ , we set the relevance score for each item  $v_m \in \mathcal{V}$  by  $\Psi_{\mathrm{RE}}(v_m) = 1 / M$ .
- FM [38] is a factorization machine-based recommendation method working on tabular data, which considers the second-order interactions among attributes (i.e., feature fields).
- DEEP FM [20] combines an FM component and a neural network component together to produce the final prediction.
- PNN [37] includes an embedding layer to learn a representation of the categorical data and a product layer to capture interactive patterns among categories.
- DIN [52] designs a deep interest network that uses a local activation unit to adaptively learn the representation of user interests from historical behaviors.
- GRU [23] applies a gated recurrent unit (GRU) to encode the long browsing histories of users.
- LSTM [18] applies a long short term memory unit (LSTM) to encode the historical browsing logs of users.
- MMOE [32] develops a multi-gate mixture-of-experts that can model the user's multiple behaviors by sharing the expert sub-models across all the behaviors.
- GCN [27] designs a graph convolutional network that learns representations of nodes (either users or items) by passing and aggregating their neighborhood information.
- GAT [46] designs a graph attention network that adopts an attention mechanism to consider the different contributions from the neighbor nodes in representing the central nodes (either users or items).
We then summarize the conversational techniques, denoted as  $\Psi_{\mathsf{CD}}(\cdot)$ , used in this paper as follows.
- AG (Abs Greedy) always queries an item with the highest relevance score at each turn, which is equivalent to solely using the recommender system as a conversational agent.
- ME (Max Entropy) always generates a query in the attribute level. In the setting of querying items and attributes, it queries the attribute with the maximum entropy, which can be formulated as:
$$
a _ {\text {q u e r y}} = \arg \max  _ {x \in \mathcal {X} _ {k - 1}} \sum_ {w _ {x} \in \mathcal {W} _ {x}} \left(\frac {\left| \mathcal {V} _ {x _ {\text {v a l u e}}} = w _ {x} \cap \mathcal {V} _ {k - 1} \right|}{\left| \mathcal {V} _ {k - 1} \right|} \log \frac {\left| \mathcal {V} _ {x _ {\text {v a l u e}}} = w _ {x} \cap \mathcal {V} _ {k - 1} \right|}{\left| \mathcal {V} _ {k - 1} \right|}\right). \tag {38}
$$
In the setting of querying items and attribute values, we first apply Eq. (38) to obtain the chosen attribute and then we select the attribute value with the highest frequency of the chose attribute as:
$$
a _ {\text {q u e r y}} = \underset {w _ {x} \in \mathcal {W} _ {x}} {\arg \max } \left| \mathcal {V} _ {x _ {\text {v a l u e}} = w _ {x}} \cap \mathcal {V} _ {k - 1} \right|, \tag {39}
$$
where xx is computed following Eq. (38). To evaluate the success rate, during the evaluation turn, we apply AG after employing ME.
- CRM [44] integrates the conversational component and the recommender component by feeding the belief tracker results to an FM-based recommendation method. It is originally designed for the single-round setting, and we follow [30] to extend it to the multiple-round setting.
- EAR [30] consists of three stages, i.e., the estimation stage to build predictive models to estimate user preference on both items and attributes based on an FM-based recommendation approach, the action stage to determine whether to query attributes or recommend items, the reflection stage to update the recommendation method.
- CRIF [25] formulates the conversational recommendation scheme as a four-phase process consisting of offline representation learning, tracking, decision, and inference. In the inference module, by fully utilizing the relation between users' attribute-level and item-level feedback, CRIF can explicitly deduce users' implicit preferences.
- UNICORN [13] formulate the conversational recommendation problem as a unified policy learning task. UNICORN uses a dynamic weighted graph-based enforcement learning method to learn a policy to select the action at each conversation turn, either asking an attribute or recommending items.
The proposed methods are listed as follows.
- CORE is our proposed method calculating  $\Psi_{\mathrm{CG}}(\cdot)$ s in line 5 in Algorithm 1.
-  $\mathsf{CORE}_{\mathsf{D}}^{+}$  is a variant of CORE that computes  $\Psi_{\mathsf{CG}}^{\mathsf{D}}(\cdot)\mathsf{s}$  instead of  $\Psi_{\mathsf{CG}}(\cdot)\mathsf{s}$ , making  $\Psi_{\mathsf{CG}}^{\mathsf{D}}(\cdot)\mathsf{s}$  consider the dependence among attributes.
A3.4 Implementation Details
For each recommendation approach, we directly follow their official implementations with the following hyper-parameter settings. The learning rate is decreased from the initial value  $1 \times 10^{-2}$  to  $1 \times 10^{-6}$  during the training process. The batch size is set as 100. The weight for the L2 regularization term is  $4 \times 10^{-5}$ . The dropout rate is set as 0.5. The dimension of embedding vectors is set as 64. For those FM-based methods (i.e., FM, DEEP FM), we build a representation vector for each attribute. We treat it as the static part of each attribute embedding, while the dynamic part is the representation of attribute values stored in the recommendation parameters. In practice, we feed the static and dynamic parts together as a whole into the model. After the training process, we store the static part and use it to estimate the dependence among attributes, as introduced in Appendix A2.2. All the models are trained under the same hardware settings with 16-Core AMD Ryzen 9 5950X (2.194GHZ), 62.78GB RAM, NVIDIA GeForce RTX 3080 cards.
A4 Additional Experimental Results
A4.1 Performance Comparisons
We conduct the experiment in two different experimental settings. One is the setting of querying items and attributes, and the other is the setting of querying items and attribute values. We report the results of the former setting on tabular datasets (i.e., Amazon, LastFM, Yelp) in Table A1, and also report the results of the latter setting on these tabular datasets in Table A2. We also evaluate the performance of CORE in sequential datasets and graph-structured datasets, and report their results in Table A3 and Table A4 respectively.
By combining these tables, our major findings are consistent with those shown in Section 4.2. Moreover, we also note that the performance of CORE in querying items and attributes is close to the oracle, and thus considering the dependence among attributes in  $\mathrm{CORE}_{\mathrm{D}}^{+}$  does not bring much improvement.